fill in the parts - whole model for the following equation.
$-9x^{3}-5x^{2}+x + 1 = (___) - (-4x^{3}+x^{2}+6x)$

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Accepted Answer

# Explanation:
## Step1: Let the unknown polynomial be $ A $. So the equation is $ -9x^3 - 5x^2 + x + 1 = A - (-4x^3 + x^2 + 6x) $.
## Step2: To find $ A $, we add $ -4x^3 + x^2 + 6x $ to both sides. So $ A = -9x^3 - 5x^2 + x + 1 + (-4x^3 + x^2 + 6x) $.
## Step3: Combine like terms. For $ x^3 $ terms: $ -9x^3 - 4x^3 = -13x^3 $. For $ x^2 $ terms: $ -5x^2 + x^2 = -4x^2 $. For $ x $ terms: $ x + 6x = 7x $. The constant term is $ 1 $. So $ A = -13x^3 - 4x^2 + 7x + 1 $.
# Answer:
$ -13x^3 - 4x^2 + 7x + 1 $

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Explanation:

Step1: Let the unknown polynomial be \( A \). So the equation is \( -9x^3 - 5x^2 + x + 1 = A - (-4x^3 + x^2 + 6x) \).

Step2: To find \( A \), we add \( -4x^3 + x^2 + 6x \) to both sides. So \( A = -9x^3 - 5x^2 + x + 1 + (-4x^3 + x^2 + 6x) \).

Step3: Combine like terms. For \( x^3 \) terms: \( -9x^3 - 4x^3 = -13x^3 \). For \( x^2 \) terms: \( -5x^2 + x^2 = -4x^2 \). For \( x \) terms: \( x + 6x = 7x \). The constant term is \( 1 \). So \( A = -13x^3 - 4x^2 + 7x + 1 \).

Answer: