What is expand 15((2x)/3+1/5)^2 ?

The solution to expand 15((2x)/3+1/5)^2 is (100x^2+60x+9)/(15)

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expand 15((2x)/3+1/5)^2

expand

15 (\frac{2 x}{3} + \frac{1}{5})^{2}

\frac{100 x ^{2} + 60 x + 9}{15}

Solution steps

15 (\frac{2 x}{3} + \frac{1}{5})^{2}

Apply Perfect Square Formula:

(a + b)^{2} = a^{2} + 2 ab + b^{2}

(\frac{2 x}{3} + \frac{1}{5})^{2} = (\frac{2 x}{3})^{2} + 2 \cdot \frac{2 x}{3} \cdot \frac{1}{5} + (\frac{1}{5})^{2}

= 15 ((\frac{2 x}{3})^{2} + 2 \cdot \frac{2 x}{3} \cdot \frac{1}{5} + (\frac{1}{5})^{2})

Simplify

(\frac{2 x}{3})^{2} + 2 \cdot \frac{2 x}{3} \cdot \frac{1}{5} + (\frac{1}{5})^{2} : \frac{100 x ^{2} + 60 x + 9}{225}

= 15 \cdot \frac{100 x ^{2} + 60 x + 9}{225}

Simplify

15 \cdot \frac{100 x ^{2} + 60 x + 9}{225} : \frac{100 x ^{2} + 60 x + 9}{15}

= \frac{100 x ^{2} + 60 x + 9}{15}

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What is expand 15((2x)/3+1/5)^2 ?
The solution to expand 15((2x)/3+1/5)^2 is (100x^2+60x+9)/(15)