(1+2x)^8(2-5x)^7

asked by guest
on Nov 24, 2024 at 12:06 pm



You asked:

Evaluate the expression: \({\left( 1 + 2 x \right)}^{8} {\left( 2 - 5 x \right)}^{7}\)

MathBot Answer:

Evaluated



\(\displaystyle {\left( 1 + 2 x \right)}^{8} {\left( 2 - 5 x \right)}^{7} = \left(2 - 5 x\right)^{7} \left(2 x + 1\right)^{8} \)

Expanded

\[{\left( 1 + 2 x \right)}^{8} {\left( 2 - 5 x \right)}^{7} = - 20000000 x^{15} - 24000000 x^{14} + 16800000 x^{13} + 28000000 x^{12} - 4620000 x^{11} - 14179200 x^{10} + 39760 x^{9} + 4054608 x^{8} + 244467 x^{7} - 709954 x^{6} - 55524 x^{5} + 76440 x^{4} + 5264 x^{3} - 4704 x^{2} - 192 x + 128\]

Factored

\[{\left( 1 + 2 x \right)}^{8} {\left( 2 - 5 x \right)}^{7} = - \left(2 x + 1\right)^{8} \left(5 x - 2\right)^{7}\]

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