Question

simplify.
$-4x^2 \left(5x^4 - 3x^2 + x - 2\
ight)$
\bigcirc $-20x^6 + 12x^4 - 4x^3 + 8x^2$
\bigcirc $-20x^6 + 12x^4 + 4x^3 - 8x^2$
\bigcirc $-20x^8 + 12x^4 - 4x^2 + 8x$
\bigcirc $-20x^6 - 12x^4 + 8x^3 - 8x^2$

Explanation:

Step1: Distribute \(-4x^2\)

Multiply \(-4x^2\) with each term inside the parentheses:

• For \(5x^4\): \(-4x^2 \cdot 5x^4 = -20x^{2 + 4} = -20x^6\)
• For \(-3x^2\): \(-4x^2 \cdot (-3x^2) = 12x^{2 + 2} = 12x^4\)
• For \(x\): \(-4x^2 \cdot x = -4x^{2 + 1} = -4x^3\)
• For \(-2\): \(-4x^2 \cdot (-2) = 8x^2\)

Step2: Combine the terms

After distribution, we get: \(-20x^6 + 12x^4 - 4x^3 + 8x^2\)

Answer:

\(-20x^6 + 12x^4 - 4x^3 + 8x^2\) (the first option)