Simplify 7b(4c-b)+4c(c-7b)

$7 b (4 c - b) + 4 c (c - 7 b)$

Step 1

Simplify each term.

Apply the distributive property.

$7 b (4 c) + 7 b (- b) + 4 c (c - 7 b)$

Rewrite using the commutative property of multiplication.

$7 \cdot 4 b c + 7 b (- b) + 4 c (c - 7 b)$

Rewrite using the commutative property of multiplication.

$7 \cdot 4 b c + 7 \cdot - 1 b \cdot b + 4 c (c - 7 b)$

Simplify each term.

Multiply $7$ by $4$ .

$28 b c + 7 \cdot - 1 b \cdot b + 4 c (c - 7 b)$

Multiply $b$ by $b$ by adding the exponents.

Move $b$ .

$28 b c + 7 \cdot - 1 (b \cdot b) + 4 c (c - 7 b)$

Multiply $b$ by $b$ .

$28 b c + 7 \cdot - 1 b^{2} + 4 c (c - 7 b)$

Multiply $7$ by $- 1$ .

$28 b c - 7 b^{2} + 4 c (c - 7 b)$

Apply the distributive property.

$28 b c - 7 b^{2} + 4 c \cdot c + 4 c (- 7 b)$

Multiply $c$ by $c$ by adding the exponents.

Move $c$ .

$28 b c - 7 b^{2} + 4 (c \cdot c) + 4 c (- 7 b)$

Multiply $c$ by $c$ .

$28 b c - 7 b^{2} + 4 c^{2} + 4 c (- 7 b)$

Rewrite using the commutative property of multiplication.

$28 b c - 7 b^{2} + 4 c^{2} + 4 \cdot - 7 c b$

Multiply $4$ by $- 7$ .

$28 b c - 7 b^{2} + 4 c^{2} - 28 c b$

Step 2

Combine the opposite terms in $28 b c - 7 b^{2} + 4 c^{2} - 28 c b$ .

Reorder the factors in the terms $28 b c$ and $- 28 c b$ .

$28 b c - 7 b^{2} + 4 c^{2} - 28 b c$

Subtract $28 b c$ from $28 b c$ .

$- 7 b^{2} + 4 c^{2} + 0$

Add $- 7 b^{2} + 4 c^{2}$ and $0$ .

$- 7 b^{2} + 4 c^{2}$