Question

How do you simplify this?


`(9k^(6)+8k^(4)-6k^(2))(4k^(2)-5)`

Answer 1

`36k^(8) -13{k}^(6) -64k^(4) + 30 {k}^(2)`

Step-by-step explanation

Recall the distributive property:

`(a + b + c)(d + e) = a(d + e) + b(d + e) + c(d + e)`

We apply this property multiple times to simplify

`(9k^(6)+8k^(4)-6k^(2))(4k^(2)-5)`

This implies that:

`9k^(6)(4k^(2)-5)+8k^(4)(4k^(2)-5)-6k^(2)(4k^(2)-5)`

We apply the distributive property again:

This time: a(b+c)=ac+ab

`\implies \: 9k^(6) * 4k^(2)-5 * 9 {k}^(6) +8k^(4) * 4k^(2)-5 * 8 {k}^(4) -6k^(2) * 4k^(2) + 5 * 6 {k}^(2)`

`\implies \: 36k^(8) -45{k}^(6) +32k^(6) -40 {k}^(4) -24k^(4) + 30 {k}^(2)`

`\implies 36k^(8) -13{k}^(6) -64k^(4) + 30 {k}^(2)`

NB:
`k^(n)*{k}^(m)=k^(m+n)`