Question

simplify the following expression.
$(x^2 - 6x - 7)(3x + 5)$
$?x^3 + \square x^2 + \square x + \square$

Explanation:

Step1: Distribute \(x^2\)

Multiply \(x^2\) by each term in \((3x + 5)\): \(x^2 \cdot 3x = 3x^3\), \(x^2 \cdot 5 = 5x^2\)

Step2: Distribute \(-6x\)

Multiply \(-6x\) by each term in \((3x + 5)\): \(-6x \cdot 3x = -18x^2\), \(-6x \cdot 5 = -30x\)

Step3: Distribute \(-7\)

Multiply \(-7\) by each term in \((3x + 5)\): \(-7 \cdot 3x = -21x\), \(-7 \cdot 5 = -35\)

Step4: Combine like terms

• For \(x^3\): Only \(3x^3\)
• For \(x^2\): \(5x^2 - 18x^2 = -13x^2\)
• For \(x\): \(-30x - 21x = -51x\)
• Constants: \(-35\)

Answer:

\(3x^3 - 13x^2 - 51x - 35\) (So the coefficient of \(x^3\) is \(3\), \(x^2\) is \(-13\), \(x\) is \(-51\), constant is \(-35\))