Expand the Trigonometric Expression (5x-4y)(10x-3y-7z)

$(5 x - 4 y) (10 x - 3 y - 7 z)$

Step 1

Expand $(5 x - 4 y) (10 x - 3 y - 7 z)$ by multiplying each term in the first expression by each term in the second expression.

$5 x (10 x) + 5 x (- 3 y) + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Step 2

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 10 x \cdot x + 5 x (- 3 y) + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

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

Move $x$ .

$5 \cdot 10 (x \cdot x) + 5 x (- 3 y) + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Multiply $x$ by $x$ .

$5 \cdot 10 x^{2} + 5 x (- 3 y) + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Multiply $5$ by $10$ .

$50 x^{2} + 5 x (- 3 y) + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Rewrite using the commutative property of multiplication.

$50 x^{2} + 5 \cdot - 3 x y + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Multiply $5$ by $- 3$ .

$50 x^{2} - 15 x y + 5 x (- 7 z) - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Rewrite using the commutative property of multiplication.

$50 x^{2} - 15 x y + 5 \cdot - 7 x z - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Multiply $5$ by $- 7$ .

$50 x^{2} - 15 x y - 35 x z - 4 y (10 x) - 4 y (- 3 y) - 4 y (- 7 z)$

Rewrite using the commutative property of multiplication.

$50 x^{2} - 15 x y - 35 x z - 4 \cdot 10 y x - 4 y (- 3 y) - 4 y (- 7 z)$

Multiply $- 4$ by $10$ .

$50 x^{2} - 15 x y - 35 x z - 40 y x - 4 y (- 3 y) - 4 y (- 7 z)$

Rewrite using the commutative property of multiplication.

$50 x^{2} - 15 x y - 35 x z - 40 y x - 4 \cdot - 3 y \cdot y - 4 y (- 7 z)$

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

Move $y$ .

$50 x^{2} - 15 x y - 35 x z - 40 y x - 4 \cdot - 3 (y \cdot y) - 4 y (- 7 z)$

Multiply $y$ by $y$ .

$50 x^{2} - 15 x y - 35 x z - 40 y x - 4 \cdot - 3 y^{2} - 4 y (- 7 z)$

Multiply $- 4$ by $- 3$ .

$50 x^{2} - 15 x y - 35 x z - 40 y x + 12 y^{2} - 4 y (- 7 z)$

Rewrite using the commutative property of multiplication.

$50 x^{2} - 15 x y - 35 x z - 40 y x + 12 y^{2} - 4 \cdot - 7 y z$

Multiply $- 4$ by $- 7$ .

$50 x^{2} - 15 x y - 35 x z - 40 y x + 12 y^{2} + 28 y z$

Step 3

Subtract $40 y x$ from $- 15 x y$ .

Move $y$ .

$50 x^{2} - 15 x y - 40 x y - 35 x z + 12 y^{2} + 28 y z$

Subtract $40 x y$ from $- 15 x y$ .

$50 x^{2} - 55 x y - 35 x z + 12 y^{2} + 28 y z$

Expand the Trigonometric Expression (5x-4y)(10x-3y-7z)

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