Algebra Examples

$(5 a - 3 c) (5 a + 3 c) - (7 c - a) (7 c + a)$

Step 1

Simplify each term.

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Step 1.1

Expand $(5 a - 3 c) (5 a + 3 c)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$5 a (5 a + 3 c) - 3 c (5 a + 3 c) - (7 c - a) (7 c + a)$

Step 1.1.2

Apply the distributive property.

$5 a (5 a) + 5 a (3 c) - 3 c (5 a + 3 c) - (7 c - a) (7 c + a)$

Step 1.1.3

Apply the distributive property.

$5 a (5 a) + 5 a (3 c) - 3 c (5 a) - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.2

Combine the opposite terms in $5 a (5 a) + 5 a (3 c) - 3 c (5 a) - 3 c (3 c)$ .

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Step 1.2.1

Reorder the factors in the terms $5 a (3 c)$ and $- 3 c (5 a)$ .

$5 a (5 a) + 3 \cdot 5 a c - 3 \cdot 5 a c - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.2.2

Subtract $3 \cdot 5 a c$ from $3 \cdot 5 a c$ .

$5 a (5 a) + 0 - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.2.3

Add $5 a (5 a)$ and $0$ .

$5 a (5 a) - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.3

Simplify each term.

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Step 1.3.1

Rewrite using the commutative property of multiplication.

$5 \cdot 5 a \cdot a - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.3.2

Multiply $a$ by $a$ by adding the exponents.

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Step 1.3.2.1

Move $a$ .

$5 \cdot 5 (a \cdot a) - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.3.2.2

Multiply $a$ by $a$ .

$5 \cdot 5 a^{2} - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.3.3

Multiply $5$ by $5$ .

$25 a^{2} - 3 c (3 c) - (7 c - a) (7 c + a)$

Step 1.3.4

Rewrite using the commutative property of multiplication.

$25 a^{2} - 3 \cdot 3 c \cdot c - (7 c - a) (7 c + a)$

Step 1.3.5

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

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Step 1.3.5.1

Move $c$ .

$25 a^{2} - 3 \cdot 3 (c \cdot c) - (7 c - a) (7 c + a)$

Step 1.3.5.2

Multiply $c$ by $c$ .

$25 a^{2} - 3 \cdot 3 c^{2} - (7 c - a) (7 c + a)$

Step 1.3.6

Multiply $- 3$ by $3$ .

$25 a^{2} - 9 c^{2} - (7 c - a) (7 c + a)$

Step 1.4

Apply the distributive property.

$25 a^{2} - 9 c^{2} + (- (7 c) - - a) (7 c + a)$

Step 1.5

Multiply $7$ by $- 1$ .

$25 a^{2} - 9 c^{2} + (- 7 c - - a) (7 c + a)$

Step 1.6

Multiply $- - a$ .

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Step 1.6.1

Multiply $- 1$ by $- 1$ .

$25 a^{2} - 9 c^{2} + (- 7 c + 1 a) (7 c + a)$

Step 1.6.2

Multiply $a$ by $1$ .

$25 a^{2} - 9 c^{2} + (- 7 c + a) (7 c + a)$

Step 1.7

Expand $(- 7 c + a) (7 c + a)$ using the FOIL Method.

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Step 1.7.1

Apply the distributive property.

$25 a^{2} - 9 c^{2} - 7 c (7 c + a) + a (7 c + a)$

Step 1.7.2

Apply the distributive property.

$25 a^{2} - 9 c^{2} - 7 c (7 c) - 7 c a + a (7 c + a)$

Step 1.7.3

Apply the distributive property.

$25 a^{2} - 9 c^{2} - 7 c (7 c) - 7 c a + a (7 c) + a \cdot a$

Step 1.8

Combine the opposite terms in $- 7 c (7 c) - 7 c a + a (7 c) + a \cdot a$ .

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Step 1.8.1

Reorder the factors in the terms $- 7 c a$ and $a (7 c)$ .

$25 a^{2} - 9 c^{2} - 7 c (7 c) - 7 a c + 7 a c + a \cdot a$

Step 1.8.2

Add $- 7 a c$ and $7 a c$ .

$25 a^{2} - 9 c^{2} - 7 c (7 c) + 0 + a \cdot a$

Step 1.8.3

Add $- 7 c (7 c)$ and $0$ .

$25 a^{2} - 9 c^{2} - 7 c (7 c) + a \cdot a$

Step 1.9

Simplify each term.

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Step 1.9.1

Rewrite using the commutative property of multiplication.

$25 a^{2} - 9 c^{2} - 7 \cdot 7 c \cdot c + a \cdot a$

Step 1.9.2

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

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Step 1.9.2.1

Move $c$ .

$25 a^{2} - 9 c^{2} - 7 \cdot 7 (c \cdot c) + a \cdot a$

Step 1.9.2.2

Multiply $c$ by $c$ .

$25 a^{2} - 9 c^{2} - 7 \cdot 7 c^{2} + a \cdot a$

Step 1.9.3

Multiply $- 7$ by $7$ .

$25 a^{2} - 9 c^{2} - 49 c^{2} + a \cdot a$

Step 1.9.4

Multiply $a$ by $a$ .

$25 a^{2} - 9 c^{2} - 49 c^{2} + a^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $25 a^{2}$ and $a^{2}$ .

$26 a^{2} - 9 c^{2} - 49 c^{2}$

Step 2.2

Subtract $49 c^{2}$ from $- 9 c^{2}$ .

$26 a^{2} - 58 c^{2}$