Question

expand the expression to a polynomial in standard form:
$(x^2 - 2x - 1)(2x^2 + 4x - 6)$

Explanation:

Step1: Distribute \(x^2\)

Multiply \(x^2\) by each term in \(2x^2 + 4x - 6\):
\(x^2 \cdot 2x^2 = 2x^4\), \(x^2 \cdot 4x = 4x^3\), \(x^2 \cdot (-6) = -6x^2\).

Step2: Distribute \(-2x\)

Multiply \(-2x\) by each term in \(2x^2 + 4x - 6\):
\(-2x \cdot 2x^2 = -4x^3\), \(-2x \cdot 4x = -8x^2\), \(-2x \cdot (-6) = 12x\).

Step3: Distribute \(-1\)

Multiply \(-1\) by each term in \(2x^2 + 4x - 6\):
\(-1 \cdot 2x^2 = -2x^2\), \(-1 \cdot 4x = -4x\), \(-1 \cdot (-6) = 6\).

Step4: Combine like terms

• \(x^4\) term: \(2x^4\)
• \(x^3\) terms: \(4x^3 - 4x^3 = 0\)
• \(x^2\) terms: \(-6x^2 - 8x^2 - 2x^2 = -16x^2\)
• \(x\) terms: \(12x - 4x = 8x\)
• Constant term: \(6\)

Answer:

\(2x^4 - 16x^2 + 8x + 6\)