What is (1/5 a^3b^2+1/2 b^5)^2 ?

The solution to (1/5 a^3b^2+1/2 b^5)^2 is (a^6b^4}{25}+\frac{a^3b^7)/5+(b^{10})/4

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simplify (1/5 a^3b^2+1/2 b^5)^2

simplify

(\frac{1}{5} a^{3} b^{2} + \frac{1}{2} b^{5})^{2}

\frac{a ^{6} b ^{4}}{25} + \frac{a ^{3} b ^{7}}{5} + \frac{b ^{10}}{4}

Solution steps

(\frac{1}{5} a^{3} b^{2} + \frac{1}{2} b^{5})^{2}

\frac{1}{5} a^{3} b^{2} = \frac{a ^{3} b ^{2}}{5}

\frac{1}{2} b^{5} = \frac{b ^{5}}{2}

= (\frac{a ^{3} b ^{2}}{5} + \frac{b ^{5}}{2})^{2}

Apply Perfect Square Formula:

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

a = \frac{a ^{3} b ^{2}}{5}, b = \frac{b ^{5}}{2}

= (\frac{a ^{3} b ^{2}}{5})^{2} + 2 \cdot \frac{a ^{3} b ^{2}}{5} \cdot \frac{b ^{5}}{2} + (\frac{b ^{5}}{2})^{2}

Simplify

(\frac{a ^{3} b ^{2}}{5})^{2} + 2 \cdot \frac{a ^{3} b ^{2}}{5} \cdot \frac{b ^{5}}{2} + (\frac{b ^{5}}{2})^{2} : \frac{a ^{6} b ^{4}}{25} + \frac{a ^{3} b ^{7}}{5} + \frac{b ^{10}}{4}

= \frac{a ^{6} b ^{4}}{25} + \frac{a ^{3} b ^{7}}{5} + \frac{b ^{10}}{4}

(- 5 x^{2} y) (3 x^{4})

\frac{- 6 x ^{2} + 2}{( x ^{2} - 1 ) ^{3}} > 0

x^{2} - 7 x - 44 = 0

3 x + x^{2}

(352 \cdot \frac{π}{180}) \cdot 4

What is (1/5 a^3b^2+1/2 b^5)^2 ?
The solution to (1/5 a^3b^2+1/2 b^5)^2 is (a^6b^4}{25}+\frac{a^3b^7)/5+(b^{10})/4