Karanveer22idn
Answered

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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​

Sagot :

XKelvinidn

Answer:

I)

[tex]\displaystyle A + B + C = 2x^2 + 4xy + 2[/tex]

II)

[tex]\displaystyle A - B + C = 6x^2 -8xy[/tex]

III)

[tex]\displaystyle A + B - C= -4x^2 + 10xy -12[/tex]

Step-by-step explanation:

We are given the three equations:

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

I)

We want to find:

[tex]\displaystyle A + B + C[/tex]

Substitute:

[tex]\displaystyle = (x^2 + xy - 6) + (6xy -2x^2 + 1) + (3x^2 + 7 -3xy)[/tex]

Rewrite:

[tex]\displaystyle = (x^2 + 3x^2 - 2x^2) + (xy + 6xy - 3xy) + (-6 + 1 + 7)[/tex]

And combine like terms. Hence:

[tex]\displaystyle A + B + C = 2x^2 + 4xy + 2[/tex]

II)

We want to find:

[tex]\displaystyle A - B + C[/tex]

Likewise, substitute:

[tex]\displaystyle = (x^2 + xy - 6) - (6xy - 2x^2 + 1) + (3x^2 + 7 - 3xy)[/tex]

Distribute:

[tex]\displaystyle = (x^2 + xy - 6) + (-6xy +2x^2 - 1) + (3x^2 + 7 - 3xy)[/tex]

Rewrite:

[tex]\displaystyle = (x^2 + 2x^2 +3x^2) + (xy - 6xy -3xy) + (-6 -1 + 7 )[/tex]

And combine like terms. Hence:

[tex]\displaystyle A - B + C = 6x^2 -8xy[/tex]

III)

We want to find:

[tex]\displaystyle A + B - C[/tex]

Substitute:

[tex]\displaystyle = (x^2 + xy - 6) + (6xy - 2x^2 + 1) - (3x^2 + 7 - 3xy)[/tex]

Distribute:

[tex]\displaystyle = (x^2 + xy - 6) + (6xy - 2x^2 + 1) + (-3x^2 - 7 + 3xy)[/tex]

Rewrite:

[tex]\displaystyle = (x^2 - 2x^2 - 3x^2) + (xy +6xy +3xy) + (-6 +1 - 7)[/tex]

And combine like terms. Hence:

[tex]\displaystyle A + B - C= -4x^2 + 10xy -12[/tex]
Hope it helped.........
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