Simplify 7x(8x^2-4y^2+3y-5)

$7 x (8 x^{2} - 4 y^{2} + 3 y - 5)$

Step 1

Apply the distributive property.

$7 x (8 x^{2}) + 7 x (- 4 y^{2}) + 7 x (3 y) + 7 x \cdot - 5$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$7 \cdot 8 x \cdot x^{2} + 7 x (- 4 y^{2}) + 7 x (3 y) + 7 x \cdot - 5$

Rewrite using the commutative property of multiplication.

$7 \cdot 8 x \cdot x^{2} + 7 \cdot - 4 x y^{2} + 7 x (3 y) + 7 x \cdot - 5$

Rewrite using the commutative property of multiplication.

$7 \cdot 8 x \cdot x^{2} + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y + 7 x \cdot - 5$

Multiply $- 5$ by $7$ .

$7 \cdot 8 x \cdot x^{2} + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$7 \cdot 8 (x^{2} x) + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

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

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

$7 \cdot 8 (x^{2} x^{1}) + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

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

$7 \cdot 8 x^{2 + 1} + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

Add $2$ and $1$ .

$7 \cdot 8 x^{3} + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

Multiply $7$ by $8$ .

$56 x^{3} + 7 \cdot - 4 x y^{2} + 7 \cdot 3 x y - 35 x$

Multiply $7$ by $- 4$ .

$56 x^{3} - 28 x y^{2} + 7 \cdot 3 x y - 35 x$

Multiply $7$ by $3$ .

$56 x^{3} - 28 x y^{2} + 21 x y - 35 x$