What is (5+4sqrt(x))^2 ?

The solution to (5+4sqrt(x))^2 is 25+40sqrt(x)+16x

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simplify (5+4sqrt(x))^2

simplify

(5 + 4 x)^{2}

25 + 40 x + 16 x

Solution steps

(5 + 4 x)^{2}

Apply Perfect Square Formula:

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

(5 + 4 x)^{2} = 5^{2} + 2 \cdot 5 \cdot 4 x + (4 x)^{2}

= 5^{2} + 2 \cdot 5 \cdot 4 x + (4 x)^{2}

5^{2} = 25

2 \cdot 5 \cdot 4 x = 40 x

(4 x)^{2} = 16 x

= 25 + 40 x + 16 x

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