What is (3/4 a^3-2/3 b^4)^2 ?

The solution to (3/4 a^3-2/3 b^4)^2 is (9a^6}{16}-a^3b^4+\frac{4b^8)/9

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simplify (3/4 a^3-2/3 b^4)^2

simplify

(\frac{3}{4} a^{3} - \frac{2}{3} b^{4})^{2}

\frac{9 a ^{6}}{16} - a^{3} b^{4} + \frac{4 b ^{8}}{9}

Solution steps

(\frac{3}{4} a^{3} - \frac{2}{3} b^{4})^{2}

Multiply

\frac{3}{4} a^{3} : \frac{3 a ^{3}}{4}

= (\frac{3 a ^{3}}{4} - \frac{2}{3} b^{4})^{2}

Multiply

\frac{2}{3} b^{4} : \frac{2 b ^{4}}{3}

= (\frac{3 a ^{3}}{4} - \frac{2 b ^{4}}{3})^{2}

Apply Perfect Square Formula:

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

a = \frac{3 a ^{3}}{4}, b = \frac{2 b ^{4}}{3}

= (\frac{3 a ^{3}}{4})^{2} - 2 \cdot \frac{3 a ^{3}}{4} \cdot \frac{2 b ^{4}}{3} + (\frac{2 b ^{4}}{3})^{2}

Simplify

(\frac{3 a ^{3}}{4})^{2} - 2 \cdot \frac{3 a ^{3}}{4} \cdot \frac{2 b ^{4}}{3} + (\frac{2 b ^{4}}{3})^{2} : \frac{9 a ^{6}}{16} - a^{3} b^{4} + \frac{4 b ^{8}}{9}

= \frac{9 a ^{6}}{16} - a^{3} b^{4} + \frac{4 b ^{8}}{9}

3 x^{2} + 1 = 54

4 y - 4 \geq 20

- 6 a^{4} b^{4} - 6 a^{3} b^{5}

(3 x + 2) 2 = (x + 2) (x - 3)

27 n^{3} - 8

What is (3/4 a^3-2/3 b^4)^2 ?
The solution to (3/4 a^3-2/3 b^4)^2 is (9a^6}{16}-a^3b^4+\frac{4b^8)/9