Solve (2x - 3y) ^ 2 + 2(2x - 3y) + (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

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

Evaluate

$2\left(2x-3y\right)\left(2x-3y+1\right)$

Solution Steps

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

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

Use the distributive property to multiply $2$ by $2x-3y$.

$$4x^{2}-12xy+9y^{2}+4x-6y+\left(2x-3y\right)^{2}$$

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

$$4x^{2}-12xy+9y^{2}+4x-6y+4x^{2}-12xy+9y^{2}$$

Combine $4x^{2}$ and $4x^{2}$ to get $8x^{2}$.

$$8x^{2}-12xy+9y^{2}+4x-6y-12xy+9y^{2}$$

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

$$8x^{2}-24xy+9y^{2}+4x-6y+9y^{2}$$

Combine $9y^{2}$ and $9y^{2}$ to get $18y^{2}$.

$$8x^{2}-24xy+18y^{2}+4x-6y$$

Expand

$8x^{2}-24xy+4x+18y^{2}-6y$

Solution Steps

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

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

Use the distributive property to multiply $2$ by $2x-3y$.

$$4x^{2}-12xy+9y^{2}+4x-6y+\left(2x-3y\right)^{2}$$

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

$$4x^{2}-12xy+9y^{2}+4x-6y+4x^{2}-12xy+9y^{2}$$

Combine $4x^{2}$ and $4x^{2}$ to get $8x^{2}$.

$$8x^{2}-12xy+9y^{2}+4x-6y-12xy+9y^{2}$$

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

$$8x^{2}-24xy+9y^{2}+4x-6y+9y^{2}$$

Combine $9y^{2}$ and $9y^{2}$ to get $18y^{2}$.

$$8x^{2}-24xy+18y^{2}+4x-6y$$