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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
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