Question

draw your own box
7 (7x + 4)(x + 7)
answer:
8 (3x + 1)(x + 7)
answer:
9 (5x + 1)(x - 2)
answer:
10 (5x - 3)(x - 3)
answer:
11 (4x + 5)(x - 5)
answer:
12 (x - 7)(4x - 7)
answer:
factors:

Explanation:

Step1: Expand using distributive property

For problem 7:

Multiply each term:

$$\begin{align*} (7x+4)(x+7) &= 7x\cdot x + 7x\cdot7 + 4\cdot x + 4\cdot7 \\ &= 7x^2 + 49x + 4x + 28 \end{align*}$$

Combine like terms:
$7x^2 + (49x+4x) + 28 = 7x^2 + 53x + 28$

Step2: Expand using distributive property

For problem 8:

Multiply each term:

$$\begin{align*} (3x+1)(x+7) &= 3x\cdot x + 3x\cdot7 + 1\cdot x + 1\cdot7 \\ &= 3x^2 + 21x + x + 7 \end{align*}$$

Combine like terms:
$3x^2 + (21x+x) + 7 = 3x^2 + 22x + 7$

Step3: Expand using distributive property

For problem 9:

Multiply each term:

$$\begin{align*} (5x+1)(x-2) &= 5x\cdot x + 5x\cdot(-2) + 1\cdot x + 1\cdot(-2) \\ &= 5x^2 - 10x + x - 2 \end{align*}$$

Combine like terms:
$5x^2 + (-10x+x) - 2 = 5x^2 - 9x - 2$

Step4: Expand using distributive property

For problem 10:

Multiply each term:

$$\begin{align*} (5x-3)(x-3) &= 5x\cdot x + 5x\cdot(-3) + (-3)\cdot x + (-3)\cdot(-3) \\ &= 5x^2 - 15x - 3x + 9 \end{align*}$$

Combine like terms:
$5x^2 + (-15x-3x) + 9 = 5x^2 - 18x + 9$

Step5: Expand using distributive property

For problem 11:

Multiply each term:

$$\begin{align*} (4x+5)(x-5) &= 4x\cdot x + 4x\cdot(-5) + 5\cdot x + 5\cdot(-5) \\ &= 4x^2 - 20x + 5x - 25 \end{align*}$$

Combine like terms:
$4x^2 + (-20x+5x) - 25 = 4x^2 - 15x - 25$

Step6: Expand using distributive property

For problem 12:

Multiply each term:

$$\begin{align*} (x-7)(4x-7) &= x\cdot4x + x\cdot(-7) + (-7)\cdot4x + (-7)\cdot(-7) \\ &= 4x^2 - 7x - 28x + 49 \end{align*}$$

Combine like terms:
$4x^2 + (-7x-28x) + 49 = 4x^2 - 35x + 49$

Answer:

Problem 7: $\boldsymbol{7x^2 + 53x + 28}$
Problem 8: $\boldsymbol{3x^2 + 22x + 7}$
Problem 9: $\boldsymbol{5x^2 - 9x - 2}$
Problem 10: $\boldsymbol{5x^2 - 18x + 9}$
Problem 11: $\boldsymbol{4x^2 - 15x - 25}$
Problem 12: $\boldsymbol{4x^2 - 35x + 49}$