Factor 16b^2+60b-100

$16 b^{2} + 60 b - 100$

Step 1

Factor $4$ out of $16 b^{2} + 60 b - 100$ .

Factor $4$ out of $16 b^{2}$ .

$4 (4 b^{2}) + 60 b - 100$

Factor $4$ out of $60 b$ .

$4 (4 b^{2}) + 4 (15 b) - 100$

Factor $4$ out of $- 100$ .

$4 (4 b^{2}) + 4 (15 b) + 4 (- 25)$

Factor $4$ out of $4 (4 b^{2}) + 4 (15 b)$ .

$4 (4 b^{2} + 15 b) + 4 (- 25)$

Factor $4$ out of $4 (4 b^{2} + 15 b) + 4 (- 25)$ .

$4 (4 b^{2} + 15 b - 25)$

Step 2

Factor.

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 4 \cdot - 25 = - 100$ and whose sum is $b = 15$ .

Factor $15$ out of $15 b$ .

$4 (4 b^{2} + 15 (b) - 25)$

Rewrite $15$ as $- 5$ plus $20$

$4 (4 b^{2} + (- 5 + 20) b - 25)$

Apply the distributive property.

$4 (4 b^{2} - 5 b + 20 b - 25)$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$4 ((4 b^{2} - 5 b) + 20 b - 25)$

Factor out the greatest common factor (GCF) from each group.

$4 (b (4 b - 5) + 5 (4 b - 5))$

Factor the polynomial by factoring out the greatest common factor, $4 b - 5$ .

$4 ((4 b - 5) (b + 5))$

Remove unnecessary parentheses.

$4 (4 b - 5) (b + 5)$

Factor 16b^2+60b-100

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