Pre-Algebra Examples

$(3 y - 8) (9 y^{2} + 24^{y} + 64)$

Step 1

Expand $(3 y - 8) (9 y^{2} + 24^{y} + 64)$ by multiplying each term in the first expression by each term in the second expression.

$3 y (9 y^{2}) + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 9 y \cdot y^{2} + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.2

Multiply $y$ by $y^{2}$ by adding the exponents.

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Step 2.1.2.1

Move $y^{2}$ .

$3 \cdot 9 (y^{2} y) + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.2.2

Multiply $y^{2}$ by $y$ .

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Step 2.1.2.2.1

Raise $y$ to the power of $1$ .

$3 \cdot 9 (y^{2} y^{1}) + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 \cdot 9 y^{2 + 1} + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.2.3

Add $2$ and $1$ .

$3 \cdot 9 y^{3} + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.3

Multiply $3$ by $9$ .

$27 y^{3} + 3 y \cdot 24^{y} + 3 y \cdot 64 - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.4

Multiply $64$ by $3$ .

$27 y^{3} + 3 y \cdot 24^{y} + 192 y - 8 (9 y^{2}) - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.5

Multiply $9$ by $- 8$ .

$27 y^{3} + 3 y \cdot 24^{y} + 192 y - 72 y^{2} - 8 \cdot 24^{y} - 8 \cdot 64$

Step 2.1.6

Multiply $- 8$ by $64$ .

$27 y^{3} + 3 y \cdot 24^{y} + 192 y - 72 y^{2} - 8 \cdot 24^{y} - 512$

Step 2.2

Reorder.

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Step 2.2.1

Move $y$ .

$27 y^{3} + 3 \cdot 24^{y} y + 192 y - 72 y^{2} - 8 \cdot 24^{y} - 512$

Step 2.2.2

Move $3 \cdot 24^{y} y$ .

$27 y^{3} + 192 y - 72 y^{2} + 3 \cdot 24^{y} y - 8 \cdot 24^{y} - 512$

Step 2.2.3

Move $192 y$ .

$27 y^{3} - 72 y^{2} + 192 y + 3 \cdot 24^{y} y - 8 \cdot 24^{y} - 512$