Algebra Examples

${(5 x - 3)}^{2}$

Step 1

Rewrite ${(5 x - 3)}^{2}$ as $(5 x - 3) (5 x - 3)$ .

$(5 x - 3) (5 x - 3)$

Step 2

Expand $(5 x - 3) (5 x - 3)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$5 x (5 x - 3) - 3 (5 x - 3)$

Step 2.2

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 3 - 3 (5 x - 3)$

Step 2.3

Apply the distributive property.

$5 x (5 x) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 x \cdot x + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3$

Step 3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.2.1

Move $x$ .

$5 \cdot 5 (x \cdot x) + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3$

Step 3.1.2.2

Multiply $x$ by $x$ .

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

Step 3.1.3

Multiply $5$ by $5$ .

$25 x^{2} + 5 x \cdot - 3 - 3 (5 x) - 3 \cdot - 3$

Step 3.1.4

Multiply $- 3$ by $5$ .

$25 x^{2} - 15 x - 3 (5 x) - 3 \cdot - 3$

Step 3.1.5

Multiply $5$ by $- 3$ .

$25 x^{2} - 15 x - 15 x - 3 \cdot - 3$

Step 3.1.6

Multiply $- 3$ by $- 3$ .

$25 x^{2} - 15 x - 15 x + 9$

Step 3.2

Subtract $15 x$ from $- 15 x$ .

$25 x^{2} - 30 x + 9$