Match Equivalent Expressions: (x+6)(x+8) and Related Forms

Question

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

Step-by-Step Solution

Let's simplify the given expressions, open the parentheses using the extended distribution law:

(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

Note that in the formula template for the above distribution law, we take by default that the operation between the terms inside the parentheses is addition, therefore we won't forget of course that the sign preceding the term is an inseparable part of it, and we'll also apply the rules of sign multiplication and thus we can present any expression in parentheses, which we'll open using the above formula, first, as an expression where addition operation exists between all terms (if required),

We will therefore simply solve each of the expressions in the given problem, while being mindful of the above, first opening the parentheses using the aforementioned distribution law and then using the commutative law of addition and multiplication and combining like terms (if there are like terms in the expression obtained after opening the parentheses):

  1. (x+6)(x+8)x⋅x+x⋅8+6⋅x+6⋅8x2+8x+6x+48x2+14x+48 (x+6)(x+8) \\ x\cdot x+x\cdot 8+6\cdot x+6\cdot8\\ x^2+8x+6x+48\\ \boxed{x^2+14x+48}\\

  2. (6+x)(8−x)↓(6+x)(8+(−x))6⋅8+6⋅(−x)+x⋅8+x⋅(−x)48−6x+8x−x248+2x−x2 (6+x)(8-x) \\ \downarrow\\ (6+x)\big(8+(-x)\big) \\ 6\cdot 8+6\cdot (-x)+x\cdot 8+x\cdot(-x)\\ 48-6x+8x-x^2\\ \boxed{48+2x-x^2}\\

  3. (x+x)(6+8)2x⋅1428x (x+x)(6+8) \\ 2x\cdot14\\ \boxed{28x}

    In the last expression we simplified above, we first combined like terms in each of the expressions within parentheses, therefore in this case there was no need to use the extended distribution law mentioned at the beginning of the solution to simplify the expression.

    Now, let's use the commutative law of addition and multiplication to observe that:

    The simplified expression in 1 matches the expression in option C,

    The simplified expression in 2 matches the expression in option A,

    The simplified expression in 3 matches the expression in option B,

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

Answer

1-b, 2-a, 3-b

More Questions

Related Subjects

The Extended Distributive Property Algebraic Method

Question Types

Extended Distributive Property: Matching expressions equal in value