Pre-Algebra Examples

$d^{4} - 2 d^{2} c^{2} + c^{4}$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $d^{4}$ as ${(d^{2})}^{2}$ .

${(d^{2})}^{2} - 2 d^{2} c^{2} + c^{4}$

Step 1.2

Rewrite $c^{4}$ as ${(c^{2})}^{2}$ .

${(d^{2})}^{2} - 2 d^{2} c^{2} + {(c^{2})}^{2}$

Step 1.3

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

$2 d^{2} c^{2} = 2 \cdot d^{2} \cdot c^{2}$

Step 1.4

Rewrite the polynomial.

${(d^{2})}^{2} - 2 \cdot d^{2} \cdot c^{2} + {(c^{2})}^{2}$

Step 1.5

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

${(d^{2} - c^{2})}^{2}$

Step 2

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

${((d + c) (d - c))}^{2}$

Step 3

Apply the product rule to $(d + c) (d - c)$ .

${(d + c)}^{2} {(d - c)}^{2}$