Pre-Algebra Examples

$(4 x - 5 y) (16 x^{2} + 20 x y + 25 y^{2})$

Step 1

Expand $(4 x - 5 y) (16 x^{2} + 20 x y + 25 y^{2})$ by multiplying each term in the first expression by each term in the second expression.

$4 x (16 x^{2}) + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

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.

$4 \cdot 16 x \cdot x^{2} + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.2

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

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Step 2.1.2.1

Move $x^{2}$ .

$4 \cdot 16 (x^{2} x) + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

$4 \cdot 16 (x^{2} x^{1}) + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.2.2.2

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

$4 \cdot 16 x^{2 + 1} + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.2.3

Add $2$ and $1$ .

$4 \cdot 16 x^{3} + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.3

Multiply $4$ by $16$ .

$64 x^{3} + 4 x (20 x y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.4

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

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Step 2.1.4.1

Move $x$ .

$64 x^{3} + 4 (x \cdot x) (20 y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.4.2

Multiply $x$ by $x$ .

$64 x^{3} + 4 x^{2} (20 y) + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$64 x^{3} + 4 \cdot 20 x^{2} y + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.6

Multiply $4$ by $20$ .

$64 x^{3} + 80 x^{2} y + 4 x (25 y^{2}) - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.7

Rewrite using the commutative property of multiplication.

$64 x^{3} + 80 x^{2} y + 4 \cdot 25 x y^{2} - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.8

Multiply $4$ by $25$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 5 y (16 x^{2}) - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.9

Rewrite using the commutative property of multiplication.

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 5 \cdot 16 y x^{2} - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.10

Multiply $- 5$ by $16$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 5 y (20 x y) - 5 y (25 y^{2})$

Step 2.1.11

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

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Step 2.1.11.1

Move $y$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 5 (y \cdot y) (20 x) - 5 y (25 y^{2})$

Step 2.1.11.2

Multiply $y$ by $y$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 5 y^{2} (20 x) - 5 y (25 y^{2})$

Step 2.1.12

Rewrite using the commutative property of multiplication.

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 5 \cdot 20 y^{2} x - 5 y (25 y^{2})$

Step 2.1.13

Multiply $- 5$ by $20$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 y (25 y^{2})$

Step 2.1.14

Rewrite using the commutative property of multiplication.

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 \cdot 25 y \cdot y^{2}$

Step 2.1.15

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

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Step 2.1.15.1

Move $y^{2}$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 \cdot 25 (y^{2} y)$

Step 2.1.15.2

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

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Step 2.1.15.2.1

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

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 \cdot 25 (y^{2} y^{1})$

Step 2.1.15.2.2

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

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 \cdot 25 y^{2 + 1}$

Step 2.1.15.3

Add $2$ and $1$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 5 \cdot 25 y^{3}$

Step 2.1.16

Multiply $- 5$ by $25$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 125 y^{3}$

Step 2.2

Combine the opposite terms in $64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 y x^{2} - 100 y^{2} x - 125 y^{3}$ .

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Step 2.2.1

Reorder the factors in the terms $80 x^{2} y$ and $- 80 y x^{2}$ .

$64 x^{3} + 80 x^{2} y + 100 x y^{2} - 80 x^{2} y - 100 y^{2} x - 125 y^{3}$

Step 2.2.2

Subtract $80 x^{2} y$ from $80 x^{2} y$ .

$64 x^{3} + 100 x y^{2} + 0 - 100 y^{2} x - 125 y^{3}$

Step 2.2.3

Add $64 x^{3} + 100 x y^{2}$ and $0$ .

$64 x^{3} + 100 x y^{2} - 100 y^{2} x - 125 y^{3}$

Step 2.2.4

Reorder the factors in the terms $100 x y^{2}$ and $- 100 y^{2} x$ .

$64 x^{3} + 100 y^{2} x - 100 y^{2} x - 125 y^{3}$

Step 2.2.5

Subtract $100 y^{2} x$ from $100 y^{2} x$ .

$64 x^{3} + 0 - 125 y^{3}$

Step 2.2.6

Add $64 x^{3}$ and $0$ .

$64 x^{3} - 125 y^{3}$