Finite Math Examples

$(y^{8} x + y^{4} + 7) (y^{4} + 4)$

Step 1

Expand $(y^{8} x + y^{4} + 7) (y^{4} + 4)$ by multiplying each term in the first expression by each term in the second expression.

$y^{8} x y^{4} + y^{8} x \cdot 4 + y^{4} y^{4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $y^{8}$ by $y^{4}$ by adding the exponents.

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Step 2.1.1.1

Move $y^{4}$ .

$y^{4} y^{8} x + y^{8} x \cdot 4 + y^{4} y^{4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.1.2

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

$y^{4 + 8} x + y^{8} x \cdot 4 + y^{4} y^{4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.1.3

Add $4$ and $8$ .

$y^{12} x + y^{8} x \cdot 4 + y^{4} y^{4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.2

Move $4$ to the left of $y^{8} x$ .

$y^{12} x + 4 \cdot (y^{8} x) + y^{4} y^{4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.3

Multiply $y^{4}$ by $y^{4}$ by adding the exponents.

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Step 2.1.3.1

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

$y^{12} x + 4 y^{8} x + y^{4 + 4} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.3.2

Add $4$ and $4$ .

$y^{12} x + 4 y^{8} x + y^{8} + y^{4} \cdot 4 + 7 y^{4} + 7 \cdot 4$

Step 2.1.4

Move $4$ to the left of $y^{4}$ .

$y^{12} x + 4 y^{8} x + y^{8} + 4 \cdot y^{4} + 7 y^{4} + 7 \cdot 4$

Step 2.1.5

Multiply $7$ by $4$ .

$y^{12} x + 4 y^{8} x + y^{8} + 4 y^{4} + 7 y^{4} + 28$

Step 2.2

Simplify by adding terms.

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Step 2.2.1

Add $4 y^{4}$ and $7 y^{4}$ .

$y^{12} x + 4 y^{8} x + y^{8} + 11 y^{4} + 28$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Reorder $y^{12}$ and $x$ .

$x y^{12} + 4 y^{8} x + y^{8} + 11 y^{4} + 28$

Step 2.2.2.2

Move $y^{8}$ .

$x y^{12} + 4 x y^{8} + y^{8} + 11 y^{4} + 28$