Question

use the area model to find the product $(-5x^{2}+2x)(-5x^{2}-2x)$. first, find the partial products. now, write the product. simplify your answer. $(-5x^{2}+2x)(-5x^{2}-2x) = \square$

Explanation:

Step1: Find partial products

• Yellow cell: Multiply \(-5x^2\) and \(-5x^2\).

\((-5x^2) \times (-5x^2) = 25x^4\)

• Cyan cell: Multiply \(-5x^2\) and \(-2x\).

\((-5x^2) \times (-2x) = 10x^3\)

• Orange cell: Multiply \(2x\) and \(-5x^2\).

\(2x \times (-5x^2) = -10x^3\)

• Pink cell: Multiply \(2x\) and \(-2x\).

\(2x \times (-2x) = -4x^2\)

Step2: Sum partial products

Add all partial products:
\(25x^4 + 10x^3 - 10x^3 - 4x^2\)

Simplify (combine like terms \(10x^3 - 10x^3 = 0\)):
\(25x^4 - 4x^2\)

Answer:

\(25x^4 - 4x^2\)