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Mathematics

Grade10

Easy

Question

Find a value for m and n to make a true statement. Select all the options that apply.
$left parenthesis m x plus n y right parenthesis squared equals 4 x squared plus 12 x y plus 9 y squared$

$m = 2, n = 3$
$m = - 2, n = 3$
$m = - 2, n = - 3$
Both a and c

hint Hint:

Compare with $left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared comma$

The correct answer is: Both a and c

Using the pattern $left parenthesis a plus b right parenthesis squared equals a squared plus 2 a b plus b squared comma$
$left parenthesis m x plus n y right parenthesis squared equals m squared x squared plus 2 m n x y plus n squared y squared$
$m squared x squared plus 2 m n x y plus n squared y squared equals 4 x squared plus 12 x y plus 9 y squared$
$m squared equals 4 comma m equals plus 2 o r minus 2$
$2 m n space equals space 12 comma space m n space equals space 6$
$n squared equals 9 comma n equals plus 3 o r minus 3$
$S o comma space m space equals space 2 space a n d space n space equals space 3 space O R space m space equals space minus 2 space a n d space n space equals space minus 3 space$

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