Factor a^2-9ab+20b^2

$a^{2} - 9 a b + 20 b^{2}$

Step 1

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 $a \cdot c = 1 \cdot 20 = 20$ and whose sum is $b = - 9$ .

Reorder terms.

$a^{2} + 20 b^{2} - 9 a b$

Reorder $20 b^{2}$ and $- 9 a b$ .

$a^{2} - 9 a b + 20 b^{2}$

Factor $- 9$ out of $- 9 a b$ .

$a^{2} - 9 (a b) + 20 b^{2}$

Rewrite $- 9$ as $- 4$ plus $- 5$

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

Apply the distributive property.

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

Remove unnecessary parentheses.

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

Remove unnecessary parentheses.

$a^{2} - 4 a b - 5 a b + 20 b^{2}$

Step 2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

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

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

$a (a - 4 b) - 5 b (a - 4 b)$

Step 3

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

$(a - 4 b) (a - 5 b)$

Factor a^2-9ab+20b^2

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