Question

If A=x² +xy-6, B=6xy-2x² +1 and C= 3x² +7 -3xy,find :(i) A+B+C​ (ii)A-B+C (iii)A+B-C​

Answer 1

Hope it helped.........

Answer 2

I)

`\displaystyle A + B + C = 2x^2 + 4xy + 2`

II)

`\displaystyle A - B + C = 6x^2 -8xy`

III)

`\displaystyle A + B - C= -4x^2 + 10xy -12`

Explanation:

We are given the three equations:

`\displaystyle A = x^2 + xy -6,\, B = 6xy - 2x^2 +1 \text{ and } C = 3x^2 + 7 -3xy`

I)

We want to find:

`\displaystyle A + B + C`

Substitute:

`\displaystyle = (x^2 + xy - 6) + (6xy -2x^2 + 1) + (3x^2 + 7 -3xy)`

Rewrite:

`\displaystyle = (x^2 + 3x^2 - 2x^2) + (xy + 6xy - 3xy) + (-6 + 1 + 7)`

And combine like terms. Hence:

`\displaystyle A + B + C = 2x^2 + 4xy + 2`

II)

We want to find:

`\displaystyle A - B + C`

Likewise, substitute:

`\displaystyle = (x^2 + xy - 6) - (6xy - 2x^2 + 1) + (3x^2 + 7 - 3xy)`

Distribute:

`\displaystyle = (x^2 + xy - 6) + (-6xy +2x^2 - 1) + (3x^2 + 7 - 3xy)`

Rewrite:

`\displaystyle = (x^2 + 2x^2 +3x^2) + (xy - 6xy -3xy) + (-6 -1 + 7 )`

And combine like terms. Hence:

`\displaystyle A - B + C = 6x^2 -8xy`

III)

We want to find:

`\displaystyle A + B - C`

Substitute:

`\displaystyle = (x^2 + xy - 6) + (6xy - 2x^2 + 1) - (3x^2 + 7 - 3xy)`

Distribute:

`\displaystyle = (x^2 + xy - 6) + (6xy - 2x^2 + 1) + (-3x^2 - 7 + 3xy)`

Rewrite:

`\displaystyle = (x^2 - 2x^2 - 3x^2) + (xy +6xy +3xy) + (-6 +1 - 7)`

And combine like terms. Hence:

`\displaystyle A + B - C= -4x^2 + 10xy -12`