Algebra Examples

$49 x^{2} - {(y + 8 x)}^{2}$

Step 1

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

${(7 x)}^{2} - {(y + 8 x)}^{2}$

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 7 x$ and $b = y + 8 x$ .

$(7 x + y + 8 x) (7 x - (y + 8 x))$

Step 3

Simplify.

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Step 3.1

Add $7 x$ and $8 x$ .

$(15 x + y) (7 x - (y + 8 x))$

Step 3.2

Apply the distributive property.

$(15 x + y) (7 x - y - (8 x))$

Step 3.3

Multiply $8$ by $- 1$ .

$(15 x + y) (7 x - y - 8 x)$

Step 3.4

Subtract $8 x$ from $7 x$ .

$(15 x + y) (- x - y)$

Step 4

Factor.

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Step 4.1

Factor $- 1$ out of $- x - y$ .

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Step 4.1.1

Factor $- 1$ out of $- x$ .

$(15 x + y) (- (x) - y)$

Step 4.1.2

Factor $- 1$ out of $- y$ .

$(15 x + y) (- (x) - (y))$

Step 4.1.3

Factor $- 1$ out of $- (x) - (y)$ .

$(15 x + y) (- (x + y))$

Step 4.2

Remove unnecessary parentheses.

$(15 x + y) \cdot - 1 (x + y)$

Step 5

Factor out negative.

$- ((15 x + y) (x + y))$

Step 6

Remove unnecessary parentheses.

$- (15 x + y) (x + y)$