Find the Product (25x^2+20xy+16y^2)(5x-4y)

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

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $25$ by $5$ .

$125 x^{3} + 25 x^{2} (- 4 y) + 20 x y (5 x) + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Rewrite using the commutative property of multiplication.

$125 x^{3} + 25 \cdot - 4 x^{2} y + 20 x y (5 x) + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Multiply $25$ by $- 4$ .

$125 x^{3} - 100 x^{2} y + 20 x y (5 x) + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

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

Move $x$ .

$125 x^{3} - 100 x^{2} y + 20 (x \cdot x) y \cdot 5 + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Multiply $x$ by $x$ .

$125 x^{3} - 100 x^{2} y + 20 x^{2} y \cdot 5 + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Multiply $5$ by $20$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y + 20 x y (- 4 y) + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

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

Move $y$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y + 20 x (y \cdot y) \cdot - 4 + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Multiply $y$ by $y$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y + 20 x y^{2} \cdot - 4 + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Multiply $- 4$ by $20$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 16 y^{2} (5 x) + 16 y^{2} (- 4 y)$

Rewrite using the commutative property of multiplication.

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 16 \cdot 5 y^{2} x + 16 y^{2} (- 4 y)$

Multiply $16$ by $5$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 y^{2} (- 4 y)$

Rewrite using the commutative property of multiplication.

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 \cdot - 4 y^{2} y$

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

Move $y$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 \cdot - 4 (y \cdot y^{2})$

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

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

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 \cdot - 4 (y^{1} y^{2})$

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

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 \cdot - 4 y^{1 + 2}$

Add $1$ and $2$ .

$125 x^{3} - 100 x^{2} y + 100 x^{2} y - 80 x y^{2} + 80 y^{2} x + 16 \cdot - 4 y^{3}$

Multiply $16$ by $- 4$ .

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

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

Add $- 100 x^{2} y$ and $100 x^{2} y$ .

$125 x^{3} + 0 - 80 x y^{2} + 80 y^{2} x - 64 y^{3}$

Add $125 x^{3}$ and $0$ .

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

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

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

Add $- 80 y^{2} x$ and $80 y^{2} x$ .

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

Add $125 x^{3}$ and $0$ .

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

Find the Product (25x^2+20xy+16y^2)(5x-4y)

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