Algebra Examples

$49 x^{2} - 84 x + 36$

Step 1

Rewrite $49 x^{2}$ as ${(7 x)}^{2}$ .

${(7 x)}^{2} - 84 x + 36$

Step 2

Rewrite $36$ as $6^{2}$ .

${(7 x)}^{2} - 84 x + 6^{2}$

Step 3

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

$84 x = 2 \cdot (7 x) \cdot 6$

Step 4

Rewrite the polynomial.

${(7 x)}^{2} - 2 \cdot (7 x) \cdot 6 + 6^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 7 x$ and $b = 6$ .

${(7 x - 6)}^{2}$