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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $3$ by $3$ .

$9 a^{4} + 3 a^{2} (7 x y) - 7 x y (3 a^{2}) - 7 x y (7 x y)$

Multiply $7$ by $3$ .

$9 a^{4} + 21 a^{2} (x y) - 7 x y (3 a^{2}) - 7 x y (7 x y)$

Multiply $3$ by $- 7$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 7 x y (7 x y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 7 (x \cdot x) y (7 y)$

Multiply $x$ by $x$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 7 x^{2} y (7 y)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 7 x^{2} (y \cdot y) \cdot 7$

Multiply $y$ by $y$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 7 x^{2} y^{2} \cdot 7$

Multiply $7$ by $- 7$ .

$9 a^{4} + 21 a^{2} x y - 21 x y a^{2} - 49 x^{2} y^{2}$

Subtract $21 x y a^{2}$ from $21 a^{2} x y$ .

Move $x$ .

$9 a^{4} + 21 a^{2} x y - 21 a^{2} x y - 49 x^{2} y^{2}$

Subtract $21 a^{2} x y$ from $21 a^{2} x y$ .

$9 a^{4} + 0 - 49 x^{2} y^{2}$

Add $9 a^{4}$ and $0$ .

$9 a^{4} - 49 x^{2} y^{2}$

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

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