Question

simplify the following expression.
$(x^2 - 8x + 7)(3x - 4)$
$?x^3 + \square x^2 + \square x + \square$

Explanation:

Step1: Distribute \(x^2\)

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

Step2: Distribute \(-8x\)

Multiply \(-8x\) by each term in \((3x - 4)\): \(-8x \cdot 3x = -24x^2\), \(-8x \cdot (-4) = 32x\)

Step3: Distribute \(7\)

Multiply \(7\) by each term in \((3x - 4)\): \(7 \cdot 3x = 21x\), \(7 \cdot (-4) = -28\)

Step4: Combine like terms

• For \(x^3\): Only \(3x^3\)
• For \(x^2\): \(-4x^2 -24x^2 = -28x^2\)
• For \(x\): \(32x + 21x = 53x\)
• For constants: \(-28\)

Answer:

\(3\) (for the \(x^3\) term), \(-28\) (for the \(x^2\) term), \(53\) (for the \(x\) term), \(-28\) (for the constant term)

So the simplified expression is \(3x^3 - 28x^2 + 53x - 28\)