Simplify (1.2c^2-7a^2)(1.2c^2+7a^2)

$(1.2 c^{2} - 7 a^{2}) (1.2 c^{2} + 7 a^{2})$

Step 1

Expand $(1.2 c^{2} - 7 a^{2}) (1.2 c^{2} + 7 a^{2})$ using the FOIL Method.

Apply the distributive property.

$1.2 c^{2} (1.2 c^{2} + 7 a^{2}) - 7 a^{2} (1.2 c^{2} + 7 a^{2})$

Apply the distributive property.

$1.2 c^{2} (1.2 c^{2}) + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2} + 7 a^{2})$

Apply the distributive property.

$1.2 c^{2} (1.2 c^{2}) + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$1.2 \cdot 1.2 c^{2} c^{2} + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

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

Move $c^{2}$ .

$1.2 \cdot 1.2 (c^{2} c^{2}) + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

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

$1.2 \cdot 1.2 c^{2 + 2} + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Add $2$ and $2$ .

$1.2 \cdot 1.2 c^{4} + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Multiply $1.2$ by $1.2$ .

$1.44 c^{4} + 1.2 c^{2} (7 a^{2}) - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Rewrite using the commutative property of multiplication.

$1.44 c^{4} + 1.2 \cdot 7 c^{2} a^{2} - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Multiply $1.2$ by $7$ .

$1.44 c^{4} + 8.4 c^{2} a^{2} - 7 a^{2} (1.2 c^{2}) - 7 a^{2} (7 a^{2})$

Rewrite using the commutative property of multiplication.

$1.44 c^{4} + 8.4 c^{2} a^{2} - 7 \cdot 1.2 a^{2} c^{2} - 7 a^{2} (7 a^{2})$

Multiply $- 7$ by $1.2$ .

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 7 a^{2} (7 a^{2})$

Rewrite using the commutative property of multiplication.

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 7 \cdot 7 a^{2} a^{2}$

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

Move $a^{2}$ .

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 7 \cdot 7 (a^{2} a^{2})$

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

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 7 \cdot 7 a^{2 + 2}$

Add $2$ and $2$ .

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 7 \cdot 7 a^{4}$

Multiply $- 7$ by $7$ .

$1.44 c^{4} + 8.4 c^{2} a^{2} - 8.4 a^{2} c^{2} - 49 a^{4}$

Subtract $8.4 a^{2} c^{2}$ from $8.4 c^{2} a^{2}$ .

Move $c^{2}$ .

$1.44 c^{4} + 8.4 a^{2} c^{2} - 8.4 a^{2} c^{2} - 49 a^{4}$

Subtract $8.4 a^{2} c^{2}$ from $8.4 a^{2} c^{2}$ .

$1.44 c^{4} + 0 a^{2} c^{2} - 49 a^{4}$

Step 3

Simplify each term.

Multiply $0$ by $a^{2}$ .

$1.44 c^{4} + 0 c^{2} - 49 a^{4}$

Multiply $0$ by $c^{2}$ .

$1.44 c^{4} + 0 - 49 a^{4}$

Step 4

Add $1.44 c^{4}$ and $0$ .

$1.44 c^{4} - 49 a^{4}$

Simplify (1.2c^2-7a^2)(1.2c^2+7a^2)

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