Pre-Algebra Examples

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

Step 1

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

$(3 y - 5) (3 y - 5)$

Step 2

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

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Step 2.1

Apply the distributive property.

$3 y (3 y - 5) - 5 (3 y - 5)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

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.

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

Step 3.1.2

Multiply $y$ by $y$ by adding the exponents.

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Step 3.1.2.1

Move $y$ .

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

Step 3.1.2.2

Multiply $y$ by $y$ .

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

Step 3.1.3

Multiply $3$ by $3$ .

$9 y^{2} + 3 y \cdot - 5 - 5 (3 y) - 5 \cdot - 5$

Step 3.1.4

Multiply $- 5$ by $3$ .

$9 y^{2} - 15 y - 5 (3 y) - 5 \cdot - 5$

Step 3.1.5

Multiply $3$ by $- 5$ .

$9 y^{2} - 15 y - 15 y - 5 \cdot - 5$

Step 3.1.6

Multiply $- 5$ by $- 5$ .

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

Step 3.2

Subtract $15 y$ from $- 15 y$ .

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