Simplify (7x^2+a^2)(x^2-3a^2)

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

Step 1

Expand $(7 x^{2} + a^{2}) (x^{2} - 3 a^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$7 x^{4} + 7 x^{2} (- 3 a^{2}) + a^{2} x^{2} + a^{2} (- 3 a^{2})$

Rewrite using the commutative property of multiplication.

$7 x^{4} + 7 \cdot - 3 x^{2} a^{2} + a^{2} x^{2} + a^{2} (- 3 a^{2})$

Multiply $7$ by $- 3$ .

$7 x^{4} - 21 x^{2} a^{2} + a^{2} x^{2} + a^{2} (- 3 a^{2})$

Rewrite using the commutative property of multiplication.

$7 x^{4} - 21 x^{2} a^{2} + a^{2} x^{2} - 3 a^{2} a^{2}$

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

Move $a^{2}$ .

$7 x^{4} - 21 x^{2} a^{2} + a^{2} x^{2} - 3 (a^{2} a^{2})$

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

$7 x^{4} - 21 x^{2} a^{2} + a^{2} x^{2} - 3 a^{2 + 2}$

Add $2$ and $2$ .

$7 x^{4} - 21 x^{2} a^{2} + a^{2} x^{2} - 3 a^{4}$

Add $- 21 x^{2} a^{2}$ and $a^{2} x^{2}$ .

Move $x^{2}$ .

$7 x^{4} - 21 a^{2} x^{2} + a^{2} x^{2} - 3 a^{4}$

Add $- 21 a^{2} x^{2}$ and $a^{2} x^{2}$ .

$7 x^{4} - 20 a^{2} x^{2} - 3 a^{4}$

Step 3

Move $7 x^{4}$ .

$- 20 a^{2} x^{2} - 3 a^{4} + 7 x^{4}$

Step 4

Reorder $- 20 a^{2} x^{2}$ and $- 3 a^{4}$ .

$- 3 a^{4} - 20 a^{2} x^{2} + 7 x^{4}$