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Mathematics

Grade10

Easy

Question

Expand.
$left parenthesis m plus 2 n right parenthesis to the power of 5$

$5 m^{5} - 10 m^{4} n - 40 m^{3} n^{2} - 80 m^{2} n^{3} + 80 m n^{4} + 32 n^{5}$
$5 m^{5} + 10 m^{4} n + 40 m^{3} n^{2} + 80 m^{2} n^{3} + 80 m n^{4} + 32 n^{5}$
$m^{5} - 10 m^{4} n + 40 m^{3} n^{2} - 80 m^{2} n^{3} + 80 m n^{4} - 32 n^{5}$
$m^{5} + 10 m^{4} n + 40 m^{3} n^{2} + 80 m^{2} n^{3} + 80 m n^{4} + 32 n^{5}$

hint Hint:

Solving using the binomial expansion.

The correct answer is: $m to the power of 5 plus 10 m to the power of 4 n plus 40 m cubed n squared plus 80 m squared n cubed plus 80 m n to the power of 4 plus 32 n to the power of 5$

STEP BY STEP SOLUTION
$open parentheses m space plus space 2 n close parentheses to the power of 5 T h e space e x p a n s i o n space o f space t h e space f o l l o w i n g space w i l l space b e space scriptbase C subscript 0 end scriptbase presuperscript 5 space m to the power of 5 space 2 n to the power of 0 space plus scriptbase C subscript 1 end scriptbase presuperscript 5 space m to the power of 4 space 2 n to the power of 1 space end exponent plus space scriptbase C subscript 2 end scriptbase presuperscript 5 space m cubed space 2 n squared space plus space scriptbase C subscript 3 space m squared space 2 n to the power of 3 space end exponent end scriptbase presuperscript 5 plus space scriptbase C subscript 4 space m to the power of 1 end scriptbase presuperscript 5 space 2 n to the power of 4 space plus scriptbase C subscript 5 space m to the power of 0 space 2 n to the power of 5 end scriptbase presuperscript 5$
$m to the power of 5 plus 10 m to the power of 4 n plus 40 m cubed n squared plus 80 m squared n cubed plus 80 m n to the power of 4 plus 32 n to the power of 5$

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