Question

Find the following product and verify the result for x=-1 and y=-2 (3x+y) (2x-1)​

Answer 1

To find  : product of $(3x+y ) (2x -1 )$  and verify for given values of $x$ and $y$ .

Given : $x = -1$ and  $y =-2$

Solution :  

• Multiplication is a process of repetitive addition of integers.
• Multiplication rules for integers :

1. If two negative integers are multiplied then the product obtained is positive integer. i.e. $(-) \times(-)=+$
2. If one negative and one positive integers are multiplied then the product obtained is negative integer. i.e. $(-) \times(+)=-$
3. If both positive integers are multiplied then the product obtained is positive integer. i.e. $(+) \times(+)=+$

• Therefore according to above rule we solve .

• $(3x+y ) (2x -1 )$   $= 6x^{2} -3x +2xy -y$

• To verify the above product for $x = -1$ and  $y =-2$

• Substituting the given values we get ,

• LHS = $(3x+y ) (2x -1 )$  

                $= [3(-1) + (-2)][2(-1)-1] \\= [-3-2][-2-1]\\=(-5)(-3 )\\= 15$

• RHS = $6x^{2} -3x +2xy -y$

                $=6(-1)^{2} -3(-1)+2(-1)(-2) -(-2) \\=6 +3+4+2\\=15$

Product of $(3x+y ) (2x -1 )$ is $6x^{2} -3x +2xy -y$  .Since , LHS = RHS hence , verified  .