Algebra Examples

9 a^{2} + 24 a b + 16 b^{2}

$9 a^{2} + 24 a b + 16 b^{2}$

Step 1

Rewrite

9 a^{2}

$9 a^{2}$ as

{(3 a)}^{2}

${(3 a)}^{2}$ .

{(3 a)}^{2} + 24 a b + 16 b^{2}

${(3 a)}^{2} + 24 a b + 16 b^{2}$

Step 2

Rewrite

16 b^{2}

$16 b^{2}$ as

{(4 b)}^{2}

${(4 b)}^{2}$ .

{(3 a)}^{2} + 24 a b + {(4 b)}^{2}

${(3 a)}^{2} + 24 a b + {(4 b)}^{2}$

Step 3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

24 a b = 2 \cdot (3 a) \cdot (4 b)

$24 a b = 2 \cdot (3 a) \cdot (4 b)$

Step 4

Rewrite the polynomial.

{(3 a)}^{2} + 2 \cdot (3 a) \cdot (4 b) + {(4 b)}^{2}

${(3 a)}^{2} + 2 \cdot (3 a) \cdot (4 b) + {(4 b)}^{2}$

Step 5

Factor using the perfect square trinomial rule

a^{2} + 2 a b + b^{2} = {(a + b)}^{2}

$a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where

a = 3 a

$a = 3 a$ and

b = 4 b

$b = 4 b$ .

{(3 a + 4 b)}^{2}

${(3 a + 4 b)}^{2}$

9 a^{2} + 24 a b + 16 b^{2}

$9 a^{2} + 24 a b + 16 b^{2}$

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