Question

Simplify the following. i) (2x-3y)(3x+y)+(x+2y)(x-y)

Answer 1

Hello friends..

problem: simplify the following (2x-3y) (3x+y)+(x+2y) (x-y)

Solution:-

(2x-3y)(3x+y) + (x+2y)(x-y)

= (6x²+2xy-9xy-3y²) + (x²-xy+2xy-2y²)

= (6x² -7xy -3y²) + (x² +xy -2y²)

= 7x² -6xy - 5y² answer

hope it helps ......

Answer 2

GIVEN :-

$\to \bf \bigg \{(2x - 3y)(3x + y) \bigg \} + \bigg \{(x + 2y)(x - y) \bigg \}$

TO FIND :-

$\to \bf \bigg \{(2x - 3y)(3x + y) \bigg \} + \bigg \{(x + 2y)(x - y) \bigg \}$

SOLUTION :-

$\to \rm \bigg \{(2x - 3y)(3x + y) \bigg \} + \bigg \{(x + 2y)(x - y) \bigg \} \\ \\ \to \rm \: \bigg \{2x(3x + y) - 3y(3x + y) \bigg \} + \bigg \{x(x - y) + 2y(x - y) \bigg \} \\ \\ \to \rm \bigg \{ 6x ^{2} + 2xy - 9xy - 3y ^{2} \bigg \} + \bigg \{x ^{2} - xy + 2xy - 2y^{2} \bigg \} \\ \\ \to \rm \: 6x ^{2} + 2xy - 9xy - 3y ^{2} + x ^{2} - xy + 2xy - 2y^{2}$

➠ Collecting like Terms,

$\to \rm \: 6x ^{2} + x ^{2} + 2xy - 9xy - xy + 2xy - 3y ^{2} - 2y ^{2} \\ \\ \to \rm \: 7x ^{2} + 2xy + 2xy - 9xy - xy - 5y ^{2} \\ \\ \to \rm \: 7x ^{2} + 4xy - 10xy - 5y ^{2} \\ \\ \to \boxed{ \red{ \bf \: 7x ^{2} - 6xy - 5y ^{2} }}$

Hence the required answer is 7x² - 6xy - 3y².

ADDITIONAL INFORMATION :-

$\to \rm ( x + y )^{2} = x^{2} + 2xy + y^{2} \\ \\ \to \rm ( x - y )^{2} = x^{2} - 2xy + y^{2} \\ \\ \to \rm ( x - y ) ( x -y ) = ( x - y )^{2} \\ \\ \to \rm ( x + y ) ( x + y ) = ( x + y )^{2} \\ \\ \to \rm x^{2} - y^{2} = ( x + y ) ( x - y )$.