Simplify (a-5w)(7a-4w)

$(a - 5 w) (7 a - 4 w)$

Step 1

Expand

$(a - 5 w) (7 a - 4 w)$ using the FOIL Method.

Apply the distributive property.

$a (7 a - 4 w) - 5 w (7 a - 4 w)$

Apply the distributive property.

$a (7 a) + a (- 4 w) - 5 w (7 a - 4 w)$

Apply the distributive property.

$a (7 a) + a (- 4 w) - 5 w (7 a) - 5 w (- 4 w)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 a \cdot a + a (- 4 w) - 5 w (7 a) - 5 w (- 4 w)$

Multiply

$a$ by

$a$ by adding the exponents.

Move

$a$ .

$7 (a \cdot a) + a (- 4 w) - 5 w (7 a) - 5 w (- 4 w)$

Multiply

$a$ by

$a$ .

$7 a^{2} + a (- 4 w) - 5 w (7 a) - 5 w (- 4 w)$

Rewrite using the commutative property of multiplication.

$7 a^{2} - 4 a w - 5 w (7 a) - 5 w (- 4 w)$

Rewrite using the commutative property of multiplication.

$7 a^{2} - 4 a w - 5 \cdot 7 w a - 5 w (- 4 w)$

Multiply

$- 5$ by

$7$ .

$7 a^{2} - 4 a w - 35 w a - 5 w (- 4 w)$

Rewrite using the commutative property of multiplication.

$7 a^{2} - 4 a w - 35 w a - 5 \cdot - 4 w \cdot w$

Multiply

$w$ by

$w$ by adding the exponents.

Move

$w$ .

$7 a^{2} - 4 a w - 35 w a - 5 \cdot - 4 (w \cdot w)$

Multiply

$w$ by

$w$ .

$7 a^{2} - 4 a w - 35 w a - 5 \cdot - 4 w^{2}$

Multiply

$- 5$ by

$- 4$ .

$7 a^{2} - 4 a w - 35 w a + 20 w^{2}$

Subtract

$35 w a$ from

$- 4 a w$ .

Move

$w$ .

$7 a^{2} - 4 a w - 35 a w + 20 w^{2}$

Subtract

$35 a w$ from

$- 4 a w$ .

$7 a^{2} - 39 a w + 20 w^{2}$

Simplify (a-5w)(7a-4w)

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