4[3-(2-4)^2+1]^3-4(3-1)^3=

asked by guest
on Jan 14, 2025 at 3:21 am



You asked:

Evaluate the expression: \(4 {\left( 3 - {\left( 2 - 4 \right)}^{2} + 1 \right)}^{3} - 4 {\left( 3 - 1 \right)}^{3}\)

MathBot Answer:

\[4 {\left( 3 - {\left( 2 - 4 \right)}^{2} + 1 \right)}^{3} - 4 {\left( 3 - 1 \right)}^{3} = -32\]

\[\begin{aligned}4 {\left( 3 - {\left( 2 - 4 \right)}^{2} + 1 \right)}^{3} - 4 {\left( 3 - 1 \right)}^{3}& = 4 \cdot \left(3 - \left(2 - 4\right)^{2} + 1\right)^{3} - 4 \cdot \left(3 - 1\right)^{3}\\& = 4 \cdot \left(3 - \left(-2\right)^{2} + 1\right)^{3} - 4 \cdot \left(3 - 1\right)^{3}\\& = 4 \cdot \left(3 - 4 + 1\right)^{3} - 4 \cdot \left(3 - 1\right)^{3}\\& = 4 \cdot \left(-1 + 1\right)^{3} - 4 \cdot \left(3 - 1\right)^{3}\\& = 4 \cdot 0^{3} - 4 \cdot \left(3 - 1\right)^{3}\\& = 4 \cdot 0 - 4 \cdot \left(3 - 1\right)^{3}\\& = 0 - 4 \cdot \left(3 - 1\right)^{3}\\& = 0 - 4 \cdot 2^{3}\\& = 0 - 4 \cdot 8\\& = 0 - 32\\& = -32\end{aligned}\]

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