Question

Match the multiplication problem on the left with the simplified polynomial on the right

Answer 1

`\begin{gathered} a)8x^3+6x^2-2x \\ b)8x^2-2x-15 \\ c)8x^2 \\ d)8x^3+16x^2-4x-15 \end{gathered}`

Explanation

remember some rule when multipling terms with exponents

`a^m\cdot a^n=a^(m+n)`

then

Step 1

make each product and compare

a)

`\begin{gathered} 2x(4x^2+3x-1) \\ 2x(4x^2)+(2x)(3x)-(2x)(1) \\ 8x^3+6x^2-2x \end{gathered}`

so, match the first expression with that result

b)

`\begin{gathered} (2x-3)(4x+5) \\ (2x)(4x)+(2x)(5)-(3)(4x)-(3)(5) \\ 8x^2+10x-12x-15 \\ 8x^2-2x-15 \end{gathered}`

so, match the first second expression with that result

c)

`\begin{gathered} 4x(2x)=(4\cdot2)x^(1+1) \\ 4x(2x)=8x^2 \end{gathered}`

d)

`\begin{gathered} (2x+3)(4x^2+2x-5) \\ (2x)(4x^2)+(2x)(2x)+(2x)(-5)+(3)(4x^2)+(3)(2x)+3(-5) \\ 8x^3+4x^2-10x+12x^2+6x-15 \\ \text{add similar terms} \\ 8x^3+16x^2-4x-15 \end{gathered}`

I hope this helps you