Factor 9p^2-42p+49

$9 p^{2} - 42 p + 49$

Step 1

Rewrite $9 p^{2}$ as ${(3 p)}^{2}$ .

${(3 p)}^{2} - 42 p + 49$

Step 2

Rewrite $49$ as $7^{2}$ .

${(3 p)}^{2} - 42 p + 7^{2}$

Step 3

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

$42 p = 2 \cdot (3 p) \cdot 7$

Step 4

Rewrite the polynomial.

${(3 p)}^{2} - 2 \cdot (3 p) \cdot 7 + 7^{2}$

Step 5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 3 p$ and $b = 7$ .

${(3 p - 7)}^{2}$