Solve (x + y) ^ 2 - (5y ^ 2 + 2xy) | 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

$$(x+y)^{2}-(5y^{2}+2xy)$$

Evaluate

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

Solution Steps

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

$$x^{2}+2xy+y^{2}-\left(5y^{2}+2xy\right)$$

To find the opposite of $5y^{2}+2xy$, find the opposite of each term.

$$x^{2}+2xy+y^{2}-5y^{2}-2xy$$

Combine $y^{2}$ and $-5y^{2}$ to get $-4y^{2}$.

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

Combine $2xy$ and $-2xy$ to get $0$.

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

Expand

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

Solution Steps

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

$$x^{2}+2xy+y^{2}-\left(5y^{2}+2xy\right)$$

To find the opposite of $5y^{2}+2xy$, find the opposite of each term.

$$x^{2}+2xy+y^{2}-5y^{2}-2xy$$

Combine $y^{2}$ and $-5y^{2}$ to get $-4y^{2}$.

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

Combine $2xy$ and $-2xy$ to get $0$.

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