Solve g ) (2x - 3y) ^ 2 - (2x + 3y) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

$-24xy$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-3y\right)^{2}$.

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

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(2x+3y\right)^{2}$.

$$4x^{2}-12xy+9y^{2}-\left(4x^{2}+12xy+9y^{2}\right)$$

To find the opposite of $4x^{2}+12xy+9y^{2}$, find the opposite of each term.

$$4x^{2}-12xy+9y^{2}-4x^{2}-12xy-9y^{2}$$

Combine $4x^{2}$ and $-4x^{2}$ to get $0$.

$$-12xy+9y^{2}-12xy-9y^{2}$$

Combine $-12xy$ and $-12xy$ to get $-24xy$.

$$-24xy+9y^{2}-9y^{2}$$

Combine $9y^{2}$ and $-9y^{2}$ to get $0$.

$$-24xy$$

Expand

$-24xy$

Solution Steps

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(2x-3y\right)^{2}$.

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

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(2x+3y\right)^{2}$.

$$4x^{2}-12xy+9y^{2}-\left(4x^{2}+12xy+9y^{2}\right)$$

To find the opposite of $4x^{2}+12xy+9y^{2}$, find the opposite of each term.

$$4x^{2}-12xy+9y^{2}-4x^{2}-12xy-9y^{2}$$

Combine $4x^{2}$ and $-4x^{2}$ to get $0$.

$$-12xy+9y^{2}-12xy-9y^{2}$$

Combine $-12xy$ and $-12xy$ to get $-24xy$.

$$-24xy+9y^{2}-9y^{2}$$

Combine $9y^{2}$ and $-9y^{2}$ to get $0$.

$$-24xy$$