Question

Find the complete factored form of the polynomial 40m^3n^2+45m^2n^6

Answer 1

Explanation:

Given expression is:

40m³n² + 45m²n⁶

We have to simplify above expression.

We use following formula to simplify above expression.

xᵃ⁺ᵇ =xᵃ.xᵇ

using above formula in given expression , we get

40m²⁺¹n² + 45m²n²⁺⁴

40m²m¹n² + 45m²n²n⁴

As 40 and 45 are multiples of 5.

5×8m²m¹n² + 5×9m²n²n⁴

taking 5m²n² as common,we get

5m²n²(8m + 9n⁴) which is the answer.

Answer 2

`=5m^(2)n^(2)(8m+9n^(4))`

Explanation:

`40m^(3)n^(2)+45m^(2)n^(6)`

Apply exponent rule:
`a^(b+c)=a^(b)a^(c)`

`m^(2)n^(6)=m^(2)n^(2)n^(4) \\m^(3)n^(2)=m^(2)mn^(2)`

`=40m^(2)mn^(2)+45m^(2)n^(2)n^(4)`

Rewrite 45 as 9*5

Rewrite 40 as 8*5

`=(8*5)m^(2)mn^(2)+ (9*5)m^(2)n^(2)n^(4)`

Factor out the common term:
`5m^(2)n^(2)`

`=5m^(2)n^(2)(8m+9n^(4))`