Question

Find the value of the expression 36x^2+25y^2-60xy when x=2/3 and y=1/5.

Answer 1

$x = \frac{2}{3} \\ y = \frac{1}{5} \\ 36 {x}^{2} + 25 {y}^{2} - 60xy \\ = {(6x)}^{2} + {(5y)}^{2} - 2 \times 6x \times 5y \\ = {(6x - 5y)}^{2} \\ = {(6 \times \frac{2}{3} - 5 \frac{1}{5}) }^{2} \\ = {(4 - 1)}^{2} \\ = {3}^{2} = 9$

Answer 2

by using identity (a-b)^2=a^2-2ab+b^2
a=6x
b=5y
(6x-5y)^2=36x^2-60xy+25y^2
x=2/3
y=1/5
(6x-5y)^2=(6×2/3-5×1/5)^2
=(4-1)^2
=3^2
=9