Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(3 x - 4 y)}^{2}$ as $(3 x - 4 y) (3 x - 4 y)$ .

$(3 x - 4 y) (3 x - 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.2

Expand $(3 x - 4 y) (3 x - 4 y)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$3 x (3 x - 4 y) - 4 y (3 x - 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.2.2

Apply the distributive property.

$3 x (3 x) + 3 x (- 4 y) - 4 y (3 x - 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.2.3

Apply the distributive property.

$3 x (3 x) + 3 x (- 4 y) - 4 y (3 x) - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x (- 4 y) - 4 y (3 x) - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.2

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

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Step 1.3.1.2.1

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x (- 4 y) - 4 y (3 x) - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.2.2

Multiply $x$ by $x$ .

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

Step 1.3.1.3

Multiply $3$ by $3$ .

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

Step 1.3.1.4

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot - 4 x y - 4 y (3 x) - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.5

Multiply $3$ by $- 4$ .

$9 x^{2} - 12 x y - 4 y (3 x) - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.6

Rewrite using the commutative property of multiplication.

$9 x^{2} - 12 x y - 4 \cdot 3 y x - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.7

Multiply $- 4$ by $3$ .

$9 x^{2} - 12 x y - 12 y x - 4 y (- 4 y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.8

Rewrite using the commutative property of multiplication.

$9 x^{2} - 12 x y - 12 y x - 4 \cdot - 4 y \cdot y - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.9

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

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Step 1.3.1.9.1

Move $y$ .

$9 x^{2} - 12 x y - 12 y x - 4 \cdot - 4 (y \cdot y) - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.9.2

Multiply $y$ by $y$ .

$9 x^{2} - 12 x y - 12 y x - 4 \cdot - 4 y^{2} - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.1.10

Multiply $- 4$ by $- 4$ .

$9 x^{2} - 12 x y - 12 y x + 16 y^{2} - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.2

Subtract $12 y x$ from $- 12 x y$ .

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Step 1.3.2.1

Move $y$ .

$9 x^{2} - 12 x y - 12 x y + 16 y^{2} - (3 x - 4 y) (3 x + 4 y)$

Step 1.3.2.2

Subtract $12 x y$ from $- 12 x y$ .

$9 x^{2} - 24 x y + 16 y^{2} - (3 x - 4 y) (3 x + 4 y)$

Step 1.4

Apply the distributive property.

$9 x^{2} - 24 x y + 16 y^{2} + (- (3 x) - (- 4 y)) (3 x + 4 y)$

Step 1.5

Multiply $3$ by $- 1$ .

$9 x^{2} - 24 x y + 16 y^{2} + (- 3 x - (- 4 y)) (3 x + 4 y)$

Step 1.6

Multiply $- 4$ by $- 1$ .

$9 x^{2} - 24 x y + 16 y^{2} + (- 3 x + 4 y) (3 x + 4 y)$

Step 1.7

Expand $(- 3 x + 4 y) (3 x + 4 y)$ using the FOIL Method.

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Step 1.7.1

Apply the distributive property.

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x + 4 y) + 4 y (3 x + 4 y)$

Step 1.7.2

Apply the distributive property.

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x) - 3 x (4 y) + 4 y (3 x + 4 y)$

Step 1.7.3

Apply the distributive property.

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x) - 3 x (4 y) + 4 y (3 x) + 4 y (4 y)$

Step 1.8

Combine the opposite terms in $- 3 x (3 x) - 3 x (4 y) + 4 y (3 x) + 4 y (4 y)$ .

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Step 1.8.1

Reorder the factors in the terms $- 3 x (4 y)$ and $4 y (3 x)$ .

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x) - 3 \cdot 4 x y + 3 \cdot 4 x y + 4 y (4 y)$

Step 1.8.2

Add $- 3 \cdot 4 x y$ and $3 \cdot 4 x y$ .

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x) + 0 + 4 y (4 y)$

Step 1.8.3

Add $- 3 x (3 x)$ and $0$ .

$9 x^{2} - 24 x y + 16 y^{2} - 3 x (3 x) + 4 y (4 y)$

Step 1.9

Simplify each term.

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Step 1.9.1

Rewrite using the commutative property of multiplication.

$9 x^{2} - 24 x y + 16 y^{2} - 3 \cdot 3 x \cdot x + 4 y (4 y)$

Step 1.9.2

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

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Step 1.9.2.1

Move $x$ .

$9 x^{2} - 24 x y + 16 y^{2} - 3 \cdot 3 (x \cdot x) + 4 y (4 y)$

Step 1.9.2.2

Multiply $x$ by $x$ .

$9 x^{2} - 24 x y + 16 y^{2} - 3 \cdot 3 x^{2} + 4 y (4 y)$

Step 1.9.3

Multiply $- 3$ by $3$ .

$9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 4 y (4 y)$

Step 1.9.4

Rewrite using the commutative property of multiplication.

$9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 4 \cdot 4 y \cdot y$

Step 1.9.5

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

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Step 1.9.5.1

Move $y$ .

$9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 4 \cdot 4 (y \cdot y)$

Step 1.9.5.2

Multiply $y$ by $y$ .

$9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 4 \cdot 4 y^{2}$

Step 1.9.6

Multiply $4$ by $4$ .

$9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 16 y^{2}$

Step 2

Simplify by adding terms.

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Step 2.1

Combine the opposite terms in $9 x^{2} - 24 x y + 16 y^{2} - 9 x^{2} + 16 y^{2}$ .

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Step 2.1.1

Subtract $9 x^{2}$ from $9 x^{2}$ .

$- 24 x y + 16 y^{2} + 0 + 16 y^{2}$

Step 2.1.2

Add $- 24 x y + 16 y^{2}$ and $0$ .

$- 24 x y + 16 y^{2} + 16 y^{2}$

Step 2.2

Add $16 y^{2}$ and $16 y^{2}$ .

$- 24 x y + 32 y^{2}$