Factor the polynomial by its greatest common monomial factor

Mathematics

1 answer:

givi [52]3 years ago

5 0

Answer:

$\large\boxed{9b^8+24b^3=(3b^3)(3b^5+8)}$

Step-by-step explanation:

$9b^8=3\cdot3\cdot b^{3+5}=\bold{3}\cdot3\cdot\bold{b^3}\cdot b^5=\bold{(3b^3)}(3b^5)\\\\24b^3=\bold3\cdot8\cdot\bold{b^3}=\bold{(3b^3)}(8)\\\\9b^8+24b^3=\bold{(3b^3)}(3b^5)+\bold{(3b^3)}(8)=\bold{(3b^3)}(3b^5+8)\\\\\text{Used}\\\\a^n\cdot a^m=a^{n+m}\\\\\text{distributive property:}\ a(b+c)=ab+ac$

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