Question

1. write in standard form $3(7x + 4)(x - 1)(x + 5)$

Explanation:

Step1: Multiply \((x - 1)\) and \((x + 5)\)

Using the distributive property \((a+b)(c+d)=ac+ad+bc+bd\), we have:
\((x - 1)(x + 5)=x\cdot x+x\cdot5-1\cdot x - 1\cdot5=x^{2}+5x - x - 5=x^{2}+4x - 5\)

Step2: Multiply \((7x + 4)\) with the result from Step1

\((7x + 4)(x^{2}+4x - 5)=7x\cdot x^{2}+7x\cdot4x+7x\cdot(-5)+4\cdot x^{2}+4\cdot4x+4\cdot(-5)\)
\(=7x^{3}+28x^{2}-35x + 4x^{2}+16x - 20\)
Combine like terms: \(7x^{3}+(28x^{2}+4x^{2})+(-35x + 16x)-20=7x^{3}+32x^{2}-19x - 20\)

Step3: Multiply the result from Step2 by 3

\(3(7x^{3}+32x^{2}-19x - 20)=3\cdot7x^{3}+3\cdot32x^{2}+3\cdot(-19x)+3\cdot(-20)\)
\(=21x^{3}+96x^{2}-57x - 60\)

Answer:

\(21x^{3}+96x^{2}-57x - 60\)