Question

if(4x-y) is a multiple of 3,show that 4x²+7xy-2y² is divisible by 9​

Answer 1

Answer:

If 4x - y is a multiple of 3 , show that 4x^2 + 7xy - 2y^3 is divisible by 9 .

4x^2 + 7xy - 2y^2 = 4x^2 + 8xy - xy - 2y^2 = 4x(x + 2y) - y(x + 2) = (4x - y)(x + 2y) Now 4x - y is divisible by 3 4x - y + 3y - 3x = x + 2y is divisible

Answer 2

Given:-

4x-y is divisible by 3

To Prove:- 4x^2+7xy-2y^2 is divisible by 9

We know that

(3)^2 = 9

So, let see that if we do (4x-y)^2, will the result be 4x^2+7xy-2y^2 or not.

Now,

(4x-y)^2

=(4x)^2-2×4x×y+(y)^2

=16x^2-8xy+y^2

Here,

4x^2+7xy-2y^2 is not equal to 16x^2-8xy+4y^2

Hence, not proved

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