Question

Multiply the two polynomials (3a² + 5a - 2)(5a² - 3a + 4)

Answer 1

The polynomials expression given are

`\mleft(3a^2+5a-2\mright)\mleft(5a^2-3a+4\mright)`

Expand the expression by distributing the parentheses

`3a^2\cdot\: 5a^2+3a^2\mleft(-3a\mright)+3a^2\cdot\: 4+5a\cdot\: 5a^2+5a\mleft(-3a\mright)+5a\cdot\: 4-2\cdot\: 5a^2-2\mleft(-3a\mright)-2\cdot\: 4`

Simplify

`\begin{gathered} 15a^4-9a^3+12a^2+25a^3-15a^2+20a-10a^2+6a-8 \\ \text{Rearranging and simplify} \\ 15a^4-9a^3+25a^3+12a^2-15a^2-10a^2+20a+6a-8 \\ 15a^4+16a^3-13a^2+26a-8 \end{gathered}`

Hence, the answer is

`15a^4+16a^3-13a^2+26a-8`