(a+b)^4-4(a+b)^2

asked by guest
on May 05, 2024 at 11:47 pm

You asked:

Evaluate the expression: \({\left( a + b \right)}^{4} - 4 \cdot {\left( a + b \right)}^{2}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( a + b \right)}^{4} - 4 \cdot {\left( a + b \right)}^{2} = \left(a + b\right)^{4} - 4 \left(a + b\right)^{2} \)

Expanded

\[{\left( a + b \right)}^{4} - 4 \cdot {\left( a + b \right)}^{2} = a^{4} + 4 a^{3} b + 6 a^{2} b^{2} - 4 a^{2} + 4 b^{3} a - 8 a b + b^{4} - 4 b^{2}\]

Factored

\[{\left( a + b \right)}^{4} - 4 \cdot {\left( a + b \right)}^{2} = \left(a + b\right)^{2} \left(a + b - 2\right) \left(a + b + 2\right)\]

asked 12 days ago

active 12 days ago