Basic Math Examples

${(3 \cdot y)}^{2} - (4 \cdot y + 7) (3 \cdot y - 8)$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $3 y$ .

$3^{2} y^{2} - (4 \cdot y + 7) (3 \cdot y - 8)$

Step 1.2

Raise $3$ to the power of $2$ .

$9 y^{2} - (4 \cdot y + 7) (3 \cdot y - 8)$

Step 1.3

Apply the distributive property.

$9 y^{2} + (- (4 y) - 1 \cdot 7) (3 \cdot y - 8)$

Step 1.4

Multiply $4$ by $- 1$ .

$9 y^{2} + (- 4 y - 1 \cdot 7) (3 \cdot y - 8)$

Step 1.5

Multiply $- 1$ by $7$ .

$9 y^{2} + (- 4 y - 7) (3 \cdot y - 8)$

Step 1.6

Expand $(- 4 y - 7) (3 y - 8)$ using the FOIL Method.

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Step 1.6.1

Apply the distributive property.

$9 y^{2} - 4 y (3 y - 8) - 7 (3 y - 8)$

Step 1.6.2

Apply the distributive property.

$9 y^{2} - 4 y (3 y) - 4 y \cdot - 8 - 7 (3 y - 8)$

Step 1.6.3

Apply the distributive property.

$9 y^{2} - 4 y (3 y) - 4 y \cdot - 8 - 7 (3 y) - 7 \cdot - 8$

Step 1.7

Simplify and combine like terms.

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Step 1.7.1

Simplify each term.

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Step 1.7.1.1

Rewrite using the commutative property of multiplication.

$9 y^{2} - 4 \cdot 3 y \cdot y - 4 y \cdot - 8 - 7 (3 y) - 7 \cdot - 8$

Step 1.7.1.2

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

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Step 1.7.1.2.1

Move $y$ .

$9 y^{2} - 4 \cdot 3 (y \cdot y) - 4 y \cdot - 8 - 7 (3 y) - 7 \cdot - 8$

Step 1.7.1.2.2

Multiply $y$ by $y$ .

$9 y^{2} - 4 \cdot 3 y^{2} - 4 y \cdot - 8 - 7 (3 y) - 7 \cdot - 8$

Step 1.7.1.3

Multiply $- 4$ by $3$ .

$9 y^{2} - 12 y^{2} - 4 y \cdot - 8 - 7 (3 y) - 7 \cdot - 8$

Step 1.7.1.4

Multiply $- 8$ by $- 4$ .

$9 y^{2} - 12 y^{2} + 32 y - 7 (3 y) - 7 \cdot - 8$

Step 1.7.1.5

Multiply $3$ by $- 7$ .

$9 y^{2} - 12 y^{2} + 32 y - 21 y - 7 \cdot - 8$

Step 1.7.1.6

Multiply $- 7$ by $- 8$ .

$9 y^{2} - 12 y^{2} + 32 y - 21 y + 56$

Step 1.7.2

Subtract $21 y$ from $32 y$ .

$9 y^{2} - 12 y^{2} + 11 y + 56$

Step 2

Subtract $12 y^{2}$ from $9 y^{2}$ .

$- 3 y^{2} + 11 y + 56$