Solve 2x(x+y)-(2x-y)^(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

$$2x(x+y)- { \left(2x-y \right) }^{ 2 }$$

Evaluate

$-2x^{2}+6xy-y^{2}$

Solution Steps

Use the distributive property to multiply $2x$ by $x+y$.

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

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

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

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

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

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

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

Combine $2xy$ and $4xy$ to get $6xy$.

$$-2x^{2}+6xy-y^{2}$$

Expand

$-2x^{2}+6xy-y^{2}$

Solution Steps

Use the distributive property to multiply $2x$ by $x+y$.

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

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

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

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

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

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

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

Combine $2xy$ and $4xy$ to get $6xy$.

$$-2x^{2}+6xy-y^{2}$$