How do you simplify $15 a^{3} b^{2} - 10 a^{2} b^{2} + 14 a^{3} b^{2} - 5 a^{2} b^{2}$ $15a^3b^2 - 10 a^2b^2 + 14a^3b^2 - 5a^2b^2$ ?

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Answer 1 · 2018-03-22T09:45:43

$a^{2} b^{2} (29 a - 15) = {(a b)}^{2} (29 a - 15)$ $a^2b^2(29a-15)=(ab)^2(29a-15)$

We need the greatest common factors in each term.

First we simplify to get: $29 a^{3} b^{2} - 15 a^{2} b^{2}$ $29a^3b^2-15a^2b^2$

There are no integers which divide into $29$ $29$ and $15$ $15$ .

$a^{2}$ $a^2$ goes into $a^{3}$ $a^3$ and $a^{2}$ $a^2$

All terms have $b^{2}$ $b^2$

So we factor out $a^{2} b^{2}$ $a^2b^2$

$a^{2} b^{2} (29 a - 15)$ $a^2b^2(29a-15)$

If you want, we can factor $a^{2} b^{2} = {(a b)}^{2}$ $a^2b^2=(ab)^2$

How do you simplify 15a^3b^2 - 10 a^2b^2 + 14a^3b^2 - 5a^2b^215a3b2−10a2b2+14a3b2−5a2b215a^3b^2 - 10 a^2b^2 + 14a^3b^2 - 5a^2b^2?