Square of sum: Transition between expressions

Equations with Variables on One SideUsing short multiplication formulasUsing variablesEquations with denominatorsComplete the missing numbersIdentify the greater valueUsing fractionsUsing quadrilateralsData with powers and rootsMore than one factorizationSystem of equations with no solutionUsing multiple rulesEquations with variables on both sidesNumber of termsSolving the problemResulting in a quadratic equation
Question 1

\( (7+x)(7+x)=\text{?} \)

Question 2

\( (x+1)^2+(x+2)^2= \)

Question 3

\( (7+8)^2=\text{?} \)

Question 4

\( (a+b)^2=\text{?} \)

Question 5

\( (3x+4)^2=\text{?} \)

Examples with solutions for Square of sum: Transition between expressions

Exercise #1

(7+x)(7+x)=? (7+x)(7+x)=\text{?}

Video Solution

Step-by-Step Solution

According to the shortened multiplication formula:

Since 7 and X appear twice, we raise both terms to the power:

(7+x)2 (7+x)^2

Answer

(7+x)2 (7+x)^2

Exercise #2

(x+1)2+(x+2)2= (x+1)^2+(x+2)^2=

Video Solution

Step-by-Step Solution

In order to solve the exercise, we will need to know the abbreviated multiplication formula:

In this exercise, we will use the formula twice:

(x+1)2=x2+2x+1 (x+1)^2=x^2+2x+1

(x+2)2=x2+4x+4 (x+2)^2=x^2+4x+4

Now, we add:

x2+2x+1+x2+4x+4=2x2+6x+5 x^2+2x+1+x^2+4x+4=2x^2+6x+5

x²+2x+1+x²+4x+4=
2x²+6x+5

Note that a common factor can be extracted from part of the digits: 2(x2+3x)+5 2(x^2+3x)+5

Answer

2(x2+3x)+5 2(x^2+3x)+5

Exercise #3

(7+8)2=? (7+8)^2=\text{?}

Video Solution

Answer

72+2×7×8+82 7^2+2\times7\times8+8^2

Exercise #4

(a+b)2=? (a+b)^2=\text{?}

Video Solution

Answer

a2+2ab+b2 a^2+2ab+b^2

Exercise #5

(3x+4)2=? (3x+4)^2=\text{?}

Video Solution

Answer

9x2+24x+16 9x^2+24x+16

Question 1

\( x^2+10x=-25 \)

Question 2

\( 4x^2=12x-9 \)

Question 3

\( 2^2+12+3^2=\text{?} \)

Question 4

Rewrite the following expression as a multiplication and as an addition:

\( (a+3b)^2 \)

Question 5

Express the following exercise as a sum and as a power:

\( (7b+3z)(7b+3z)=\text{?} \)

Exercise #6

x2+10x=−25 x^2+10x=-25

Video Solution

Answer

x=−5 x=-5

Exercise #7

4x2=12x−9 4x^2=12x-9

Video Solution

Answer

x=32 x=\frac{3}{2}

Exercise #8

22+12+32=? 2^2+12+3^2=\text{?}

Video Solution

Answer

(2+3)2 (2+3)^2

Exercise #9

Rewrite the following expression as a multiplication and as an addition:

(a+3b)2 (a+3b)^2

Video Solution

Answer

(a+3b)(a+3b) (a+3b)(a+3b)

a2+6ab+9b2 a^2+6ab+9b^2

Exercise #10

Express the following exercise as a sum and as a power:

(7b+3z)(7b+3z)=? (7b+3z)(7b+3z)=\text{?}

Video Solution

Answer

49b2+42bz+9z2 49b^2+42bz+9z^2

(7b+3z)2 (7b+3z)^2

Question 1

Solve for y:

\( y^2+4y+2=-2 \)

Question 2

Solve for x:

\( x^2+32x=-256 \)

Exercise #11

Solve for y:

y2+4y+2=−2 y^2+4y+2=-2

Video Solution

Answer

y=−2 y=-2

Exercise #12

Solve for x:

x2+32x=−256 x^2+32x=-256

Video Solution

Answer

x=−16 x=-16