Fully simplify. (3x^(2)+y^(3))^(2) 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: (3x^(2) + y^(3))^2 = (3x^(2))^2 + 2*(3x^(2))*(y^(3)) + (y^(3))^2.Combine Results: Calculate each term separately: (3x^(2))^2 = 9x^(4) (since (3^2)*(x^(2*2)) = 9x^(4)), 2*(3x^(2))*(y^(3)) = 6x^(2)y^(3) (since 2*3*x^(2)*y^(3) = 6x^(2)y^(3)), (y^(3))^2 = y^(6) (since (y^(3))^2 = y^(3*2) = y^(6)).Combine the results from Step 3 to get the final simplified expression: (3x^(2) + y^(3))^2 = 9x^(4) + 6x^(2)y^(3) + y^(6).

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Grade 8

Relationship between squares and square roots

Full solution

Q. Fully simplify.

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

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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: $\newline$ $(3x^{2} + y^{3})^{2} = 9x^{4} + 6x^{2}y^{3} + y^{6}$ .