Algebra Examples

$(24 x^{4} - 15 x^{2} + 6 x) - (10 x^{4} + 5 x^{2} - 4 x)$

Step 1

Remove parentheses.

$24 x^{4} - 15 x^{2} + 6 x - (10 x^{4} + 5 x^{2} - 4 x)$

Step 2

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

$24 {(x^{2})}^{2} - 15 x^{2} + 6 x - (10 x^{4} + 5 x^{2} - 4 x)$

Step 3

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

$24 {(x^{2})}^{2} - 15 x^{2} + 6 x - (10 {(x^{2})}^{2} + 5 x^{2} - 4 x)$

Step 4

Let $u = x^{2}$ . Substitute $u$ for all occurrences of $x^{2}$ .

$14 u^{2} - 20 u + 10 x$

Step 5

Factor $2$ out of $14 u^{2} - 20 u + 10 x$ .

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Step 5.1

Factor $2$ out of $14 u^{2}$ .

$2 (7 u^{2}) - 20 u + 10 x$

Step 5.2

Factor $2$ out of $- 20 u$ .

$2 (7 u^{2}) + 2 (- 10 u) + 10 x$

Step 5.3

Factor $2$ out of $10 x$ .

$2 (7 u^{2}) + 2 (- 10 u) + 2 (5 x)$

Step 5.4

Factor $2$ out of $2 (7 u^{2}) + 2 (- 10 u)$ .

$2 (7 u^{2} - 10 u) + 2 (5 x)$

Step 5.5

Factor $2$ out of $2 (7 u^{2} - 10 u) + 2 (5 x)$ .

$2 (7 u^{2} - 10 u + 5 x)$

Step 6

Replace all occurrences of $u$ with $x^{2}$ .

$2 (7 {(x^{2})}^{2} - 10 x^{2} + 5 x)$

Step 7

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 7.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 (7 x^{2 \cdot 2} - 10 x^{2} + 5 x)$

Step 7.2

Multiply $2$ by $2$ .

$2 (7 x^{4} - 10 x^{2} + 5 x)$

Step 8

Factor.

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Step 8.1

Factor $x$ out of $7 x^{4} - 10 x^{2} + 5 x$ .

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Step 8.1.1

Factor $x$ out of $7 x^{4}$ .

$2 (x (7 x^{3}) - 10 x^{2} + 5 x)$

Step 8.1.2

Factor $x$ out of $- 10 x^{2}$ .

$2 (x (7 x^{3}) + x (- 10 x) + 5 x)$

Step 8.1.3

Factor $x$ out of $5 x$ .

$2 (x (7 x^{3}) + x (- 10 x) + x \cdot 5)$

Step 8.1.4

Factor $x$ out of $x (7 x^{3}) + x (- 10 x)$ .

$2 (x (7 x^{3} - 10 x) + x \cdot 5)$

Step 8.1.5

Factor $x$ out of $x (7 x^{3} - 10 x) + x \cdot 5$ .

$2 (x (7 x^{3} - 10 x + 5))$

Step 8.2

Remove unnecessary parentheses.

$2 x (7 x^{3} - 10 x + 5)$