Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Rewrite using the commutative property of multiplication.

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

Step 1.3

Rewrite using the commutative property of multiplication.

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

Step 1.4

Simplify each term.

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Step 1.4.1

Multiply $7$ by $4$ .

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

Step 1.4.2

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

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Step 1.4.2.1

Move $b$ .

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

Step 1.4.2.2

Multiply $b$ by $b$ .

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

Step 1.4.3

Multiply $7$ by $- 1$ .

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

Step 1.5

Apply the distributive property.

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

Step 1.6

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

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Step 1.6.1

Move $c$ .

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

Step 1.6.2

Multiply $c$ by $c$ .

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

Step 1.7

Rewrite using the commutative property of multiplication.

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

Step 1.8

Multiply $4$ by $- 7$ .

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

Step 2

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

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Step 2.1

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

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

Step 2.2

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

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

Step 2.3

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

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