Question

If A=4x²+y²-6xy B=3y²+12x²+8xy C=6x²+8y²+6xy
find A+B+C and 2A-B​

Answer 1

There you go!! Hope it helps!

Answer 2

Step-by-step explanation:

Given:-

A=4x^2+y^2-6xy

B=3y^2+12x^2+8xy

C=6x^2+8y^2+6xy

To find:-

Find A+B+C and 2A-B ?

Solution:-

Given that :-

A=4x^2+y^2-6xy

B=3y^2+12x^2+8xy

It can be written as

B= 12x^2+3y^2+8xy

C=6x^2+8y^2+6xy

1) A+B+C:-

Horizontal method:-

(4x^2+y^2-6xy)+(12x^2+3y^2+8xy)+(6x^2+8y^2+6xy)

=> (4x^2+12x^2+6x^2)+(y^2+3y^2+8y^2)+(-6xy+8xy+6xy)

=> (4+12+6)x^2+(1+3+8)y^2+(-6+8+6)xy

=> 22x^2+12y^2+8xy

A+B+C = 22x^2+12y^2+8xy

Vertical method:-

4x^2 + y^2 - 6xy

12x^2 + 3y^2 + 8xy

6x^2 + 8y^2 + 6xy

(+)

__________________

22x^2 + 12y^2 + 8xy

__________________

2) 2A-B :-

2A = 2×A

=> 2×(4x^2+y^2-6xy)

=> 8x^2+2y^2-12xy

Now,

Horizontal method:-

2A-B = (8x^2+2y^2-12xy)-(12x^2+3y^2+8xy)

=> 8x^2+2y^2-12xy-12x^2-3y^2-8xy

=> (8x^2-12x^2)+(2y^2-3y^2)+(-12xy-8xy)

=> (8-12)x^2+(2-3)y^2+(-12-8)xy

=> (-4)x^2+(-1)y^2+(-20)xy

=> -4x^2-y^2-20xy

Vertical method:-:-

8x^2+2y^2-12xy

12x^2+3y^2+8xy

(-)

______________

-4x^2-y^2-20xy

______________

Answer:-

1) The value of A+B+C for the given problem is 22x^2+12y^2+ 8xy

2) The value of 2A-B is -4x^2-y^2-20xy

Used Methods:-

• Horizontal method

• Vertical method

Used Concept:-

• When subtract an expression from another expression then change the symbols of the second expression and add it.i.e. write the additive inverses of the terms in the second expression and then adding them .