Question

simplify the following expression.
$(x^2 + 9x - 3)(5x + 1)$
$?x^3 + \square x^2 + \square x + \square$

Explanation:

Step1: Multiply \(x^2\) by each term in \((5x + 1)\)

\(x^2 \times 5x = 5x^3\), \(x^2 \times 1 = x^2\)

Step2: Multiply \(9x\) by each term in \((5x + 1)\)

\(9x \times 5x = 45x^2\), \(9x \times 1 = 9x\)

Step3: Multiply \(-3\) by each term in \((5x + 1)\)

\(-3 \times 5x = -15x\), \(-3 \times 1 = -3\)

Step4: Combine like terms

• For \(x^3\) term: Only \(5x^3\)
• For \(x^2\) term: \(x^2 + 45x^2 = 46x^2\)
• For \(x\) term: \(9x - 15x = -6x\)
• Constant term: \(-3\)

Answer:

\(5x^3 + 46x^2 - 6x - 3\) (So the coefficients are 5, 46, -6, -3 respectively for \(x^3\), \(x^2\), \(x\), and constant term)