Extended Distributive Property: Matching expressions equal in value

Solving the problemUsing a rectangleDistributive property in geometrySolving an equation using the extended distributive lawUsing additional geometric shapesAscertain whether the law of distributive property is applicableIs the equality correct?Using variablesComplete the missing numberApplying the formula
Question 1

Match the expressions (numbers) with the equivalent expressions (letters):

  1. \( (2x-y)(x+3) \)

  2. \( (y-2x)(3-x) \)

  3. \( (2x+y)(x-3) \)

    a.\( 2x^2-6x+yx-3y \)

    b.\( 2x^2-6x-yx+3y \)

    c.\( 2x^2+6x-yx-3y \)

Question 2

Join expressions of equal value

  1. \( (a-b)(c-4) \)

  2. \( (a+b)(c+4) \)

  3. \( (a-b)(c+4) \)

  4. \( (a+b)(c-4) \)

    a.\( ac-4a+bc-4b \)

    b.\( ac+4a-bc-4b \)

    c.\( ac-4a-bc+4b \)

    d.\( ac+4a+bc+4b \)

Question 3

Join expressions that have the same value

  1. \( (x+4)(x-3) \)

  2. \( (x+4)(x+3) \)

  3. \( (x-4)(x-3) \)

    a.\( x^2+x-12 \)

    b.\( x^2-7x+12 \)

    c.\( x^2+7x+12 \)

Question 4

Match the expressions that have the same value:

  1. \( (2x+y)(x+2y) \)

  2. \( (2x+2y)(x+y) \)

  3. \( (2x-y)(x-2y) \)

    a. \( 2x^2+4xy+2y^2 \)

    b. \( 2x^2-5xy+2y^2 \)

    c. \( 2x^2+5xy+2y^2 \)

Question 5

Join expressions of equal value

  1. \( (a+b)(c+d) \)

  2. \( (a+c)(b+d) \)

  3. \( (a+d)(c+b) \)

    a.\( ac+ad+bc+bd \)

    b.\( ac+ab+dc+db \)

    c.\( ab+ad+cb+cd \)

Examples with solutions for Extended Distributive Property: Matching expressions equal in value

Exercise #1

Match the expressions (numbers) with the equivalent expressions (letters):

  1. (2x−y)(x+3) (2x-y)(x+3)

  2. (y−2x)(3−x) (y-2x)(3-x)

  3. (2x+y)(x−3) (2x+y)(x-3)

    a.2x2−6x+yx−3y 2x^2-6x+yx-3y

    b.2x2−6x−yx+3y 2x^2-6x-yx+3y

    c.2x2+6x−yx−3y 2x^2+6x-yx-3y

Video Solution

Step-by-Step Solution

Simplify the given expressions, open parentheses using the extended distributive property:

(a+b)(c+d)=ac+ad+bc+bd (\textcolor{red}{a}+\textcolor{blue}{b})(c+d)=\textcolor{red}{a}c+\textcolor{red}{a}d+\textcolor{blue}{b}c+\textcolor{blue}{b}d Keep in mind that in the formula form for the distributive property mentioned above, we assume by default that the operation between the terms inside the parentheses is an addition, therefore, of course, we will not forget that the sign of the term's coefficient is an inseparable part of it. Furthermore, we will apply the rules of sign multiplication and thus we can present any expression within parentheses, which is opened with the help of the previous formula, first, as an expression in which an addition operation takes place among all the terms (if necessary),

Then we will simplify each and every one of the expressions of the given problem, respecting the above, first opening the parentheses through the previously mentioned distributive property. Then we will use the substitution property in addition and multiplication before introducing like terms (if there are like terms in the expression obtained after opening the parentheses):

  1. (2x−y)(x+3)↓(2x+(−y))(x+3)2x⋅x+2x⋅3+(−y)⋅x+(−y)⋅32x2+6x−yx−3y (2x-y)(x+3) \\ \downarrow\\ \big(2x+(-y)\big)(x+3) \\ 2x\cdot x+2x\cdot 3+(-y)\cdot x+(-y)\cdot3\\ \boxed{2x^2+6x-yx-3y}\\

  2. (y−2x)(3−x)↓(y+(−2x))(3+(−x))y⋅3+y⋅(−x)+(−2x)⋅3+(−2x)⋅(−x)3y−xy−6x+2x2 (y-2x)(3-x) \\ \downarrow\\ \big(y+(-2x)\big)\big(3+(-x)\big) \\ y\cdot 3+y\cdot (-x)+(-2x)\cdot 3+(-2x)\cdot(-x)\\ \boxed{3y-xy-6x+2x^2}\\

  3. (2x+y)(x−3)↓(2x+y)(x+(−3))2x⋅x+2x⋅(−3)+y⋅x+y⋅(−3)2x2−6x+yx−3y (2x+y)(x-3) \\ \downarrow\\ (2x+y)(x+(-3)) \\ 2x\cdot x+2x\cdot (-3)+y\cdot x+y\cdot(-3)\\ \boxed{2x^2-6x+yx-3y}\\ As you can notice, in all the expressions where we applied multiplication between the expressions in the previous parentheses, the result of the multiplication (obtained after applying the previously mentioned distributive property) produced an expression in which terms cannot be added, and this is because all the terms in the resulting expression are different from each other (remember that all like variables must be identical and in the same power),

    Now, let's use the substitution property in addition and multiplication to distinguish that:

    The simplified expression in 1 corresponds to the expression in option C,

    The simplified expression in 2 corresponds to the expression in option B,

    The simplified expression in 3 corresponds to the expression in option A,

Therefore, the correct answer (among the options offered) is option B.

Answer

1-b, 2-c, 3-a

Exercise #2

Join expressions of equal value

  1. (a−b)(c−4) (a-b)(c-4)

  2. (a+b)(c+4) (a+b)(c+4)

  3. (a−b)(c+4) (a-b)(c+4)

  4. (a+b)(c−4) (a+b)(c-4)

    a.ac−4a+bc−4b ac-4a+bc-4b

    b.ac+4a−bc−4b ac+4a-bc-4b

    c.ac−4a−bc+4b ac-4a-bc+4b

    d.ac+4a+bc+4b ac+4a+bc+4b

Video Solution

Step-by-Step Solution

We use all the exercises of the extended distributive property:(a+b)×(c+d)=ac+ad+bc+bd (a+b)\times(c+d)=ac+ad+bc+bd

1.(a−b)(c−4)=ac−4a−bc+4b (a-b)(c-4)=ac-4a-bc+4b

2.(a+b)(c+4)=ac+4a+bc+4b (a+b)(c+4)=ac+4a+bc+4b

3.(a−b)(c+4)=ac+4a−bc−4b (a-b)(c+4)=ac+4a-bc-4b

4.(a+b)(c−4)=ac−4a+bc−4b (a+b)(c-4)=ac-4a+bc-4b

Answer

1-c, 2-d, 3-b, 4-a

Exercise #3

Join expressions that have the same value

  1. (x+4)(x−3) (x+4)(x-3)

  2. (x+4)(x+3) (x+4)(x+3)

  3. (x−4)(x−3) (x-4)(x-3)

    a.x2+x−12 x^2+x-12

    b.x2−7x+12 x^2-7x+12

    c.x2+7x+12 x^2+7x+12

Video Solution

Answer

1-a, 2-c, 3-b

Exercise #4

Match the expressions that have the same value:

  1. (2x+y)(x+2y) (2x+y)(x+2y)

  2. (2x+2y)(x+y) (2x+2y)(x+y)

  3. (2x−y)(x−2y) (2x-y)(x-2y)

    a. 2x2+4xy+2y2 2x^2+4xy+2y^2

    b. 2x2−5xy+2y2 2x^2-5xy+2y^2

    c. 2x2+5xy+2y2 2x^2+5xy+2y^2

Video Solution

Answer

1-c, 2-a, 3-b

Exercise #5

Join expressions of equal value

  1. (a+b)(c+d) (a+b)(c+d)

  2. (a+c)(b+d) (a+c)(b+d)

  3. (a+d)(c+b) (a+d)(c+b)

    a.ac+ad+bc+bd ac+ad+bc+bd

    b.ac+ab+dc+db ac+ab+dc+db

    c.ab+ad+cb+cd ab+ad+cb+cd

Video Solution

Answer

1-a, 2-b, 3-b

Question 1

Join expressions of equal value

  1. \( (m-n)(a-4) \)

  2. \( (4-n)(m+a) \)

  3. \( (n-m)(4-a) \)

    a.\( 4m+4a-nm-na \)

    b.\( ma-4m-na+4n \)

    c.\( -ma+4m+na-4n \)

Question 2

Join expressions of equal value

  1. \( (x+6)(x+8) \)

  2. \( (6+x)(8-x) \)

  3. \( (x+x)(6+8) \)

    a.\( 48+2x-x^2 \)

    b.\( 28x \)

    c.\( x^2+14x+48 \)

Question 3

Join expressions of equal value

  1. \( (a+g)x+3 \)

  2. \( (x+3)(a+g) \)

  3. \( (a-g)x-3 \)

    a.\( xa+xg+3a+3g \)

    b.\( ax+gx+3 \)

    c.\( ax-gx-3 \)

Question 4

Join expressions of equal value

  1. \( (2x+9)(y+4) \)

  2. \( (2y+9)(x+4) \)

  3. \( (2x-9)(y-4) \)

  4. \( (2x+9)(y-4) \)

    a.\( 2xy+8x+9y+36 \)

    b.\( 2xy-8x+9y-36 \)

    c.\( 2xy-8x-9y+36 \)

    d.\( 2xy+8y+9x+36 \)

Question 5

Join expressions of equal value

  1. \( 3(y+b)+4x \)

  2. \( (3+4x)(y+b) \)

  3. \( (4y+3)(x+b) \)

    a.\( 3y+3b+4x \)

    b.\( 4yx+4yb+3x+3b \)

    c.\( 3y+3b+4xy+4xb \)

Exercise #6

Join expressions of equal value

  1. (m−n)(a−4) (m-n)(a-4)

  2. (4−n)(m+a) (4-n)(m+a)

  3. (n−m)(4−a) (n-m)(4-a)

    a.4m+4a−nm−na 4m+4a-nm-na

    b.ma−4m−na+4n ma-4m-na+4n

    c.−ma+4m+na−4n -ma+4m+na-4n

Video Solution

Answer

1=3=b, 2=a

Exercise #7

Join expressions of equal value

  1. (x+6)(x+8) (x+6)(x+8)

  2. (6+x)(8−x) (6+x)(8-x)

  3. (x+x)(6+8) (x+x)(6+8)

    a.48+2x−x2 48+2x-x^2

    b.28x 28x

    c.x2+14x+48 x^2+14x+48

Video Solution

Answer

1-b, 2-a, 3-b

Exercise #8

Join expressions of equal value

  1. (a+g)x+3 (a+g)x+3

  2. (x+3)(a+g) (x+3)(a+g)

  3. (a−g)x−3 (a-g)x-3

    a.xa+xg+3a+3g xa+xg+3a+3g

    b.ax+gx+3 ax+gx+3

    c.ax−gx−3 ax-gx-3

Video Solution

Answer

1-b, 2-a, 3-c

Exercise #9

Join expressions of equal value

  1. (2x+9)(y+4) (2x+9)(y+4)

  2. (2y+9)(x+4) (2y+9)(x+4)

  3. (2x−9)(y−4) (2x-9)(y-4)

  4. (2x+9)(y−4) (2x+9)(y-4)

    a.2xy+8x+9y+36 2xy+8x+9y+36

    b.2xy−8x+9y−36 2xy-8x+9y-36

    c.2xy−8x−9y+36 2xy-8x-9y+36

    d.2xy+8y+9x+36 2xy+8y+9x+36

Video Solution

Answer

4-b, 3-c, 2-d, 1-a

Exercise #10

Join expressions of equal value

  1. 3(y+b)+4x 3(y+b)+4x

  2. (3+4x)(y+b) (3+4x)(y+b)

  3. (4y+3)(x+b) (4y+3)(x+b)

    a.3y+3b+4x 3y+3b+4x

    b.4yx+4yb+3x+3b 4yx+4yb+3x+3b

    c.3y+3b+4xy+4xb 3y+3b+4xy+4xb

Video Solution

Answer

1-a, 2-c, 3-b

Question 1

Join expressions of equal value

  1. \( (y+5)(x+7) \)

  2. \( (x+5)(y+7) \)

  3. \( (x-5)(y-7) \)

  4. \( (x-5)(y+7) \)

    a.\( xy+7y+5x+35 \)

    b.\( xy+7x+5y+35 \)

    c.\( xy-7x-5y+35 \)

    d.\( xy+7x-5y-35 \)

Question 2

Join expressions of equal value

  1. \( (12x-5)(y+2) \)

  2. \( (x-12)(5y+2) \)

  3. \( (12x+5)(y-2) \)

    a.\( 12xy-24x+5y-10 \)

    b.\( 12xy+24x-5y-10 \)

    c.\( 5xy+2x-60y-24 \)

Question 3

Join expressions of equal value

  1. \( (4+x)(y+8+x) \)

  2. \( (4+x+y)(8+x) \)

  3. \( (12+x)(y+x) \)

    a.\( x^2+12x+xy+12y \)

    b.\( x^2+12x+xy+4y+32 \)

    c.\( x^2+12x+xy+8y+32 \)

Question 4

Join expressions of equal value

  1. \( (-7-x)(a-13) \)

  2. \( (-a+13)(-7-x) \)

  3. \( (7+x)(a-13) \)

    a.\( 7a+ax-91-13x \)

    b.\( -7a+91-ax+13x \)

    c.\( 7a-ax+91-13x \)

Question 5

Join expressions of equal value

  1. \( (2a+b)(b+4) \)

  2. \( (4+a)(2b+b) \)

  3. \( (2a-b)(b-4) \)

  4. \( (2a-b)(b+4) \)

    a.\( 2ab-8a-b^2+4b \)

    b.\( 12b+3ab \)

    c.\( 2ab+8a-b^2-4b \)

    d.\( 2ab+8a+b^2+4b \)

Exercise #11

Join expressions of equal value

  1. (y+5)(x+7) (y+5)(x+7)

  2. (x+5)(y+7) (x+5)(y+7)

  3. (x−5)(y−7) (x-5)(y-7)

  4. (x−5)(y+7) (x-5)(y+7)

    a.xy+7y+5x+35 xy+7y+5x+35

    b.xy+7x+5y+35 xy+7x+5y+35

    c.xy−7x−5y+35 xy-7x-5y+35

    d.xy+7x−5y−35 xy+7x-5y-35

Video Solution

Answer

1-a, 2-b, 3-c, 4-d

Exercise #12

Join expressions of equal value

  1. (12x−5)(y+2) (12x-5)(y+2)

  2. (x−12)(5y+2) (x-12)(5y+2)

  3. (12x+5)(y−2) (12x+5)(y-2)

    a.12xy−24x+5y−10 12xy-24x+5y-10

    b.12xy+24x−5y−10 12xy+24x-5y-10

    c.5xy+2x−60y−24 5xy+2x-60y-24

Video Solution

Answer

1-c, 2-b, 3-a

Exercise #13

Join expressions of equal value

  1. (4+x)(y+8+x) (4+x)(y+8+x)

  2. (4+x+y)(8+x) (4+x+y)(8+x)

  3. (12+x)(y+x) (12+x)(y+x)

    a.x2+12x+xy+12y x^2+12x+xy+12y

    b.x2+12x+xy+4y+32 x^2+12x+xy+4y+32

    c.x2+12x+xy+8y+32 x^2+12x+xy+8y+32

Video Solution

Answer

1-c, 2-b, 3-a

Exercise #14

Join expressions of equal value

  1. (−7−x)(a−13) (-7-x)(a-13)

  2. (−a+13)(−7−x) (-a+13)(-7-x)

  3. (7+x)(a−13) (7+x)(a-13)

    a.7a+ax−91−13x 7a+ax-91-13x

    b.−7a+91−ax+13x -7a+91-ax+13x

    c.7a−ax+91−13x 7a-ax+91-13x

Video Solution

Answer

1-b, 2,3-a

Exercise #15

Join expressions of equal value

  1. (2a+b)(b+4) (2a+b)(b+4)

  2. (4+a)(2b+b) (4+a)(2b+b)

  3. (2a−b)(b−4) (2a-b)(b-4)

  4. (2a−b)(b+4) (2a-b)(b+4)

    a.2ab−8a−b2+4b 2ab-8a-b^2+4b

    b.12b+3ab 12b+3ab

    c.2ab+8a−b2−4b 2ab+8a-b^2-4b

    d.2ab+8a+b2+4b 2ab+8a+b^2+4b

Video Solution

Answer

1-d, 2-b, 3-a, 4-c

Question 1

Group the expressions that have the same value.

  1. \( (b+c)(a-4) \)

  2. \( (4+c)(a+b) \)

  3. \( (a+4)(b-c) \)

  4. \( (b+4)(c-a) \)

    a. \( ac+ab-4b-4c \)

    b. \( 4b+ab-4c-ac \)

    c. \( bc-ab+4c-4a \)

    d. \( 4a+4b+ac+cb \)

Exercise #16

Group the expressions that have the same value.

  1. (b+c)(a−4) (b+c)(a-4)

  2. (4+c)(a+b) (4+c)(a+b)

  3. (a+4)(b−c) (a+4)(b-c)

  4. (b+4)(c−a) (b+4)(c-a)

    a. ac+ab−4b−4c ac+ab-4b-4c

    b. 4b+ab−4c−ac 4b+ab-4c-ac

    c. bc−ab+4c−4a bc-ab+4c-4a

    d. 4a+4b+ac+cb 4a+4b+ac+cb

Video Solution

Answer

1-a, 2-d, 3-b, 4-c