simplify fully, (x^2+4)^2-(x^2-2)^2

asked by guest
on Apr 10, 2025 at 1:26 am



You asked:

Simplify the expression: (x2+4)2−(x2−2)2{\left( {x}^{2} + 4 \right)}^{2} - {\left( {x}^{2} - 2 \right)}^{2}

MathBot Answer:

Simplified:

(x2+4)2−(x2−2)2=−(x2−2)2+(x2+4)2 {\left( {x}^{2} + 4 \right)}^{2} - {\left( {x}^{2} - 2 \right)}^{2} = - \left(x^{2} - 2\right)^{2} + \left(x^{2} + 4\right)^{2}

(x2+4)2−(x2−2)2=−(x4−4x2+4)+(x2+4)2=x4+8x2+16−x4−4x2+4=−x4+4x2−4+x4+8x2+16=12x2+12\begin{aligned}\left(x^{2} + 4\right)^{2} - \left(x^{2} - 2\right)^{2}&=-\left(x^{4} - 4 x^{2} + 4\right) + \left(x^{2} + 4\right)^{2}\\&=x^{4} + 8 x^{2} + 16 - x^{4} - 4 x^{2} + 4\\&=- x^{4} + 4 x^{2} - 4 + x^{4} + 8 x^{2} + 16\\&=12 x^{2} + 12\end{aligned}

Expanded:

(x2+4)2−(x2−2)2=12x2+12 {\left( {x}^{2} + 4 \right)}^{2} - {\left( {x}^{2} - 2 \right)}^{2} = 12 x^{2} + 12


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