Find the following products and verify the result for $x = -1, y = -2$:
$(3x-5y)(x+y)$

Given:

$(3x-5y)(x+y)$

To do:

We have to find the given product and verify the result for $x = -1, y = -2$.

Solution:

We know that,

$(a+b)\times(c+d)=a(c+d)+b(c+d)$

Therefore,

$(3x-5y)(x+y) = 3x \times (x + y) - 5y \times (x + y)$

$= 3x \times x + 3x \times y-5y \times x-5y \times y$

$= 3x^2 + 3xy - 5xy - 5y^2$

$= 3x^2 - 2xy - 5y^2$

LHS $= (3x-5y)(x+y)$

$= [3 (-1) -5 (-2)] [-1 +(-2)]$

$= (-3 + 10) (-3)$

$= 7 \times (-3)$

$= -21$

RHS $= 3x^2 - 2xy - 5y^2$

$= 3 (-1)^2 - 2 (-1) (-2) -5(-2)^2$

$=3(1)-4-5(4)$

$=3-4-20$

$= 3-24$

$= -21$

Therefore,

LHS $=$ RHS