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

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

Evaluate

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

Solution Steps

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

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

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

$$4n^{2}-12nx+9x^{2}+4n-6y+2n-3y$$

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

$$4n^{2}-12nx+9x^{2}+6n-6y-3y$$

Combine $-6y$ and $-3y$ to get $-9y$.

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

Expand

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

Solution Steps

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

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

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

$$4n^{2}-12nx+9x^{2}+4n-6y+2n-3y$$

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

$$4n^{2}-12nx+9x^{2}+6n-6y-3y$$

Combine $-6y$ and $-3y$ to get $-9y$.

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