Solve 9(x)^(2)+2xy+((y)^(2))/(9) | 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

$$9 { x }^{ 2 } +2xy+ \frac{ { y }^{ 2 } }{ 9 }$$

Evaluate

$\frac{\left(9x+y\right)^{2}}{9}$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply $9x^{2}+2xy$ times $\frac{9}{9}$.

$$\frac{9\left(9x^{2}+2xy\right)}{9}+\frac{y^{2}}{9}$$

Since $\frac{9\left(9x^{2}+2xy\right)}{9}$ and $\frac{y^{2}}{9}$ have the same denominator, add them by adding their numerators.

$$\frac{9\left(9x^{2}+2xy\right)+y^{2}}{9}$$

Do the multiplications in $9\left(9x^{2}+2xy\right)+y^{2}$.

$$\frac{81x^{2}+18xy+y^{2}}{9}$$

Factor

$\frac{\left(9x+y\right)^{2}}{9}$

Solution Steps

Factor out $\frac{1}{9}$.

$$\frac{81x^{2}+18xy+y^{2}}{9}$$

Consider $81x^{2}+18xy+y^{2}$. Use the perfect square formula, $a^{2}+2ab+b^{2}=\left(a+b\right)^{2}$, where $a=9x$ and $b=y$.

$$\left(9x+y\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(9x+y\right)^{2}}{9}$$