Solve (2x + 3y) ^ 2 + (6x - 5y) ^ 2 | Equatix - Math Solver

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Example

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

a⋅(b-2)=3b

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a⋅(b-2)=3b

Question

$$(2x+3y)^{2}+(6x-5y)^{2}$$

Evaluate

$40x^{2}-48xy+34y^{2}$

Solution Steps

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

$$4x^{2}+12xy+9y^{2}+\left(6x-5y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(6x-5y\right)^{2}$.

$$4x^{2}+12xy+9y^{2}+36x^{2}-60xy+25y^{2}$$

Combine $4x^{2}$ and $36x^{2}$ to get $40x^{2}$.

$$40x^{2}+12xy+9y^{2}-60xy+25y^{2}$$

Combine $12xy$ and $-60xy$ to get $-48xy$.

$$40x^{2}-48xy+9y^{2}+25y^{2}$$

Combine $9y^{2}$ and $25y^{2}$ to get $34y^{2}$.

$$40x^{2}-48xy+34y^{2}$$

Expand

$40x^{2}-48xy+34y^{2}$

Solution Steps

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

$$4x^{2}+12xy+9y^{2}+\left(6x-5y\right)^{2}$$

Use binomial theorem $\left(a-b\right)^{2}=a^{2}-2ab+b^{2}$ to expand $\left(6x-5y\right)^{2}$.

$$4x^{2}+12xy+9y^{2}+36x^{2}-60xy+25y^{2}$$

Combine $4x^{2}$ and $36x^{2}$ to get $40x^{2}$.

$$40x^{2}+12xy+9y^{2}-60xy+25y^{2}$$

Combine $12xy$ and $-60xy$ to get $-48xy$.

$$40x^{2}-48xy+9y^{2}+25y^{2}$$

Combine $9y^{2}$ and $25y^{2}$ to get $34y^{2}$.

$$40x^{2}-48xy+34y^{2}$$