Pre-Algebra Examples

$x^{2} - \frac{8}{7} \cdot (x y) + \frac{16}{49} y^{2}$

Step 1

Factor $\frac{1}{49}$ out of each term.

$\frac{1}{49} (49 x^{2} - 56 y x + 16 y^{2})$

Step 2

Factor using the perfect square rule.

Tap for more steps...

Step 2.1

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

$\frac{1}{49} \cdot ({(7 x)}^{2} - 56 y x + 16 y^{2})$

Step 2.2

Rewrite $16 y^{2}$ as ${(4 y)}^{2}$ .

$\frac{1}{49} \cdot ({(7 x)}^{2} - 56 y x + {(4 y)}^{2})$

Step 2.3

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

$56 y x = 2 \cdot (7 x) \cdot (4 y)$

Step 2.4

Rewrite the polynomial.

$\frac{1}{49} \cdot ({(7 x)}^{2} - 2 \cdot (7 x) \cdot (4 y) + {(4 y)}^{2})$

Step 2.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 7 x$ and $b = 4 y$ .

$\frac{1}{49} \cdot {(7 x - 4 y)}^{2}$