Question

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

Answer 1

Answer:

$=5m^{2}n^{2}(8m+9n^{4})$

Step-by-step 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:$5m^{2}n^{2}$

$=5m^{2}n^{2}(8m+9n^{4})$

Answer 2

Answer:

Step-by-step 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.