Basic Math Examples

${(2 a - b)}^{2} - {(48 c - 16 d)}^{2}$

Step 1

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 2 a - b$ and $b = 48 c - 16 d$ .

$(2 a - b + 48 c - 16 d) (2 a - b - (48 c - 16 d))$

Step 2

Simplify.

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Step 2.1

Apply the distributive property.

$(2 a - b + 48 c - 16 d) (2 a - b - (48 c) - (- 16 d))$

Step 2.2

Multiply $48$ by $- 1$ .

$(2 a - b + 48 c - 16 d) (2 a - b - 48 c - (- 16 d))$

Step 2.3

Multiply $- 16$ by $- 1$ .

$(2 a - b + 48 c - 16 d) (2 a - b - 48 c + 16 d)$