multiplying polynomials {coloring activity!} name: sharon castillo date: 1-28-26 per: 7,8 set 1 simplify each expression. then, find the sum of your answers in each row. 1 ((x + 4)(x + 7)) ((x + 8)(x + 5)) 2 ((x + 9)(x - 2)) ((x + 6)(x - 3)) 3 ((x - 5)(x + 6)) ((x - 2)(x + 1)) 4 ((x - 4)(x - 1)) ((x - 7)(x - 5)) 5 ((2x - 10)(x + 3)) ((3x + 1)(x - 4)) 6 ((4x - 5)(x - 2)) ((x - 5)(x - 5)) set 2 simplify each expression. then, find the difference of your answers in each row. 7 ((7x + 3)(x - 9)) ((5x + 3)(x + 1)) 8 ((2x + 1)(2x - 1)) ((x + 4)(x - 4)) 9 ((4x + 1)(3x - 7)) ((3x - 4)(2x - 8)) 10 ((3x - 1)^2) ((x + 6)^2) 11 ((x - 2)(x^2 + 8x - 1)) ((x + 4)(x^2 - 5x + 9)) 12 ((3x + 5)(x^2 - 10x + 2)) ((2x - 1)(x^2 - 3x - 7)) match the question number with the answer below. color the picture accordingly. red: (2x^2 - 32) yellow: (5x^2 - 15x - 34) orange: (3x^2 + 15) light green: (8x^2 - 18x - 35) dark green: (2x^2 + 24x + 68) light blue: (x^3 - 18x^2 - 33x + 3) dark blue: (2x^2 - 68x - 30) purple: (7x^2 - 6x - 34) pink: (2x^2 - 17x + 39) brown: (2x^2 + 10x - 36) black: (6x^2 + 7x - 39) gray: (5x^2 - 23x + 35) © gina wilson (all things algebra), 201

Question

Accepted Answer

Let's solve the first problem in Set 1: $(x + 4)(x + 7)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
Multiply the First terms: $x \times x = x^2$
Multiply the Outer terms: $x \times 7 = 7x$
Multiply the Inner terms: $4 \times x = 4x$
Multiply the Last terms: $4 \times 7 = 28$
So, $(x + 4)(x + 7) = x^2 + 7x + 4x + 28$

## Step 2: Combine like terms
Combine the $x$ terms: $7x + 4x = 11x$
So, the simplified form is $x^2 + 11x + 28$

# Answer:
$x^2 + 11x + 28$

Now, let's solve the second problem in Set 1: $(x + 8)(x + 5)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
Multiply the First terms: $x \times x = x^2$
Multiply the Outer terms: $x \times 5 = 5x$
Multiply the Inner terms: $8 \times x = 8x$
Multiply the Last terms: $8 \times 5 = 40$
So, $(x + 8)(x + 5) = x^2 + 5x + 8x + 40$

## Step 2: Combine like terms
Combine the $x$ terms: $5x + 8x = 13x$
So, the simplified form is $x^2 + 13x + 40$

# Answer:
$x^2 + 13x + 40$

For the sum of the answers in row 1 (Set 1):
$(x^2 + 11x + 28) + (x^2 + 13x + 40)$

# Explanation:
## Step 1: Combine like terms for $x^2$
$x^2 + x^2 = 2x^2$

## Step 2: Combine like terms for $x$
$11x + 13x = 24x$

## Step 3: Combine constant terms
$28 + 40 = 68$

So, the sum is $2x^2 + 24x + 68$

# Answer:
$2x^2 + 24x + 68$

Let's solve the first problem in Set 2: $(7x + 3)(x - 9)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
Multiply the First terms: $7x \times x = 7x^2$
Multiply the Outer terms: $7x \times (-9) = -63x$
Multiply the Inner terms: $3 \times x = 3x$
Multiply the Last terms: $3 \times (-9) = -27$
So, $(7x + 3)(x - 9) = 7x^2 - 63x + 3x - 27$

## Step 2: Combine like terms
Combine the $x$ terms: $-63x + 3x = -60x$
So, the simplified form is $7x^2 - 60x - 27$

# Answer:
$7x^2 - 60x - 27$

The second problem in Set 2: $(5x + 3)(x + 1)$

# Explanation:
## Step 1: Use the distributive property (FOIL method)
Multiply the First terms: $5x \times x = 5x^2$
Multiply the Outer terms: $5x \times 1 = 5x$
Multiply the Inner terms: $3 \times x = 3x$
Multiply the Last terms: $3 \times 1 = 3$
So, $(5x + 3)(x + 1) = 5x^2 + 5x + 3x + 3$

## Step 2: Combine like terms
Combine the $x$ terms: $5x + 3x = 8x$
So, the simplified form is $5x^2 + 8x + 3$

# Answer:
$5x^2 + 8x + 3$

For the difference of the answers in row 1 (Set 2):
$(7x^2 - 60x - 27) - (5x^2 + 8x + 3)$

# Explanation:
## Step 1: Distribute the negative sign
$7x^2 - 60x - 27 - 5x^2 - 8x - 3$

## Step 2: Combine like terms for $x^2$
$7x^2 - 5x^2 = 2x^2$

## Step 3: Combine like terms for $x$
$-60x - 8x = -68x$

## Step 4: Combine constant terms
$-27 - 3 = -30$

So, the difference is $2x^2 - 68x - 30$

# Answer:
$2x^2 - 68x - 30$

These are the solutions for the first row in both sets. You can follow similar steps to solve the remaining problems.

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QUESTION IMAGE

Question

Explanation:

Step 1: Use the distributive property (FOIL method)

Step 2: Combine like terms

Step 1: Use the distributive property (FOIL method)

Step 2: Combine like terms

Step 1: Combine like terms for \(x^2\)

Step 2: Combine like terms for \(x\)

Step 3: Combine constant terms

Answer: