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Fully simplify.

(3x^(2)+y^(3))^(2)
Answer:

Fully simplify. $\newline$ $\left(3 x^{2}+y^{3}\right)^{2}$ $\newline$ Answer:

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Relationship between squares and square roots

Full solution

Q. Fully simplify.

\newline

\left(3 x^{2}+y^{3}\right)^{2}

\newline

Answer:

Apply Binomial Expansion: We have the expression $(3x^{2} + y^{3})^{2}$ . To simplify this, we need to apply the binomial expansion formula $(a + b)^{2} = a^{2} + 2ab + b^{2}$ , where $a$ is $3x^{2}$ and $b$ is $y^{3}$ .
Calculate Terms: Apply the binomial expansion to the expression: $\newline$ egin{equation}( $3$ x^{ $2$ } + y^{ $3$ })^{ $2$ } = ( $3$ x^{ $2$ })^{ $2$ } + $2$ \cdot ( $3$ x^{ $2$ }) \cdot (y^{ $3$ }) + (y^{ $3$ })^{ $2$ }. $\newline$ egin{equation}
Combine Results: Calculate each term separately: $\newline$ $(3x^{2})^{2} = 9x^{4}$ (since $(3^{2})\cdot(x^{2\cdot2}) = 9x^{4}$ ), $\newline$ $2\cdot(3x^{2})\cdot(y^{3}) = 6x^{2}y^{3}$ (since $2\cdot3\cdot x^{2}\cdot y^{3} = 6x^{2}y^{3}$ ), $\newline$ $(y^{3})^{2} = y^{6}$ (since $(y^{3})^{2} = y^{3\cdot2} = y^{6}$ ).
Combine Results: Calculate each term separately: $\newline$ $(3x^{2})^{2} = 9x^{4}$ (since $(3^{2})\cdot(x^{2\cdot2}) = 9x^{4}$ ), $\newline$ $2\cdot(3x^{2})\cdot(y^{3}) = 6x^{2}y^{3}$ (since $2\cdot3\cdot x^{2}\cdot y^{3} = 6x^{2}y^{3}$ ), $\newline$ $(y^{3})^{2} = y^{6}$ (since $(y^{3})^{2} = y^{3\cdot2} = y^{6}$ ).Combine the results from Step $3$ to get the final simplified expression: $\newline$ $(3x^{2} + y^{3})^{2} = 9x^{4} + 6x^{2}y^{3} + y^{6}$ .

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