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\(A+B+C=4x^2-5xy+5y^2+3x^2+2xy+y^2+x^2+3xy+2y^2\)
\(=\left(4x^2+3x^2+x^2\right)+\left(-5xy+2xy+3xy\right)+\left(5y^2+y^2+2y^2\right)\)
\(=8x^2+8y^2\)
\(B-C-A=\left(3x^2+2xy+y^2\right)-\left(x^2+3xy+2y^2\right)-\left(4x^2-5xy+5y^2\right)\)
\(=3x^2+2xy+y^2-x^2-3xy-2y^2-4x^2+5xy-5y^2\)
\(=\left(3x^2-x^2-4x^2\right)+\left(2xy-3xy+5xy\right)+\left(y^2-2y^2-5y^2\right)\)
\(=-2x^2+4xy-6y^2\)
\(C-A-B=\left(x^2+3xy+2y^2\right)-\left(4x^2-5xy+5y^2\right)-\left(3x^2+2xy+y^2\right)\)
\(=x^2+3xy+2y^2-4x^2+5xy-5y^2-3x^2-2xy-y^2\)
\(=\left(x^2-4x^2-3x^2\right)+\left(3xy+5xy-2xy\right)+\left(2y^2-5y^2-y^2\right)\)
\(=-6x^2+6xy-4y^2\)
\(A+B-C=4x^2-5xy+5y^2+3x^2+2xy+y^2-\left(x^2+3xy+2y^2\right)\)
\(=4x^2-5xy+5y^2+3x^2+2xy+y^2-x^2-3xy-2y^2\)
\(=\left(4x^2+3x^2-x^2\right)+\left(-5xy+2xy-3xy\right)+\left(5y^2+y^2-2y^2\right)\)
\(=6x^2-6xy+4y^2\)
a/ \(A+B+C=\left(4x^2-5xy+3y^2\right)+\left(3x^2+2xy+y^2\right)+\left(2y^2+3xy-x^2\right)\)
\(=\left(4x^2+3x^2-x^2\right)+\left(-5xy+2xy+3xy\right)+\left(3y^2+y^2+2y^2\right)\)
\(=6x^2+6y^2\)
b/ \(B-C-A=\left(3x^2+2xy+y^2\right)-\left(2y^2+3xy-x^2\right)-\left(4x^2-5xy+3y^2\right)\)
\(=\left(3x^2+x^2-4x^2\right)+\left(2xy-3xy+5xy\right)+\left(y^2+2y^2-3y^2\right)\)
\(=-4xy\)
c/ \(C-A-B=\left(2y^2+3xy-x^2\right)-\left(4x^2-5xy+3y^2\right)-\left(3x^2+2xy+y^2\right)\)
\(=\left(2y^2-3y^2-y^2\right)+\left(3xy+5xy-2xy\right)+\left(-x^2+4x^2-3x^2\right)\)
\(=-2y+6xy\)
Sửa đề: \(B=3x^2+2xy+y^2\)
\(A+B+C=6x^2+6y^2\)
\(B-C-A=3x^2+2xy+y^2+x^2-3xy-2y^2-4x^2+5xy-3y^2\)
\(=4x^2-xy-y^2-4x^2+5xy-3y^2\)
\(=4xy-4y^2\)
A + B + C = ( 4x2 - 5xy + 3y2 ) + ( 3x2 + 2xy + y2 ) + ( -x2 + 3xy + 2y2 )
= 4x2 - 5xy + 3y2 + 3x2 + 2xy + y2 - x2 + 3xy + 2y2
= ( 4x2 - 3x2 - x2 ) + ( 5xy + 2xy + 3xy ) + ( 3y2 + y2 + 2y2 )
= 10xy + 6y2
B - C - A = ( 3x2 + 2xy + y2 ) - ( -x2 + 3xy + 2y2 ) - ( 4x2 - 5xy + 3y2 )
= 3x2 + 2xy + y2 + x2 - 3xy - 2y2 - 4x2 + 5xy - 3y2
= ( 3x2 + x2 - 4x2 ) - ( 2xy - 3xy + 5xy ) - ( y2 - 2y2 - 3y2 )
= 0 - 0 - ( -4y2 )
= 0 + 4y2
= 4y2
C - A - B = ( -x2 + 3xy + 2y2 ) - ( 4x2 - 5xy + 3y2 ) - ( 3x2 + 2xy + y2 )
= -x2 + 3xy + 2y2 - 4x2 + 5xy - 3y2 - 3x2 - 2xy - y2
= ( -x2 - 4x2 - 3x2 ) - ( 3xy + 5xy - 2xy ) - ( 2y2 - 3y2 - y2 )
= -8x2 - 6xy - ( -2y2 )
= -8x2 - 6xy + 2y2
* Lần đầu làm xD Sai sót gì mong bạn thông cảm *
a, A+B+C = ( 4x^2-5xy+3y^2 ) + ( 3x^2+2xy+y^2 ) + ( -x^2+3xy+2y^2 )
= 4x^2-5xy+3y^2 + 3x^2+2xy+y^2 - x^2+3xy+2y^2
= ( 4x^2 + 3x^2 - x^2 ) + ( -5xy + 2xy + 3xy ) + ( 3y^2 + y^2 + 2y^2 )
= 6x^2 + 6y^2
b, B-C-A = ( 3x^2+2xy+y^2 ) - ( -x^2+3xy+2y^2 ) - ( 4x^2-5xy+3y^2 )
= 3x^2+2xy+y^2 + x^2+3xy+2y^2 - 4x^2-5xy+3y^2
= ( 3x^2 + x^2 - 4x^2 ) + ( 2xy + 3xy - 5xy ) + ( y^2 + 2y^2 + 3y^2 )
= 6y^2
c,C-A-B = ( -x^2+3xy+2y^2 ) - ( 4x^2-5xy+3y^2 ) - ( 3x^2+2xy+y^2 )
= -x^2+3xy+2y^2 - 4x^2-5xy+3y^2 - 3x^2+2xy+y^2
= ( -x^2 - 4x^2 - 3x^2 ) + ( 3xy -5xy + 2xy ) + ( 2y^2 + 3y^2 + y^2 )
= -8x^2 + 6y^2
Bài tập 2:
a/ A + (x2 - 2xy + y2) = x2 +2xy + y2
=> A = (x2 + 2xy + y2) - (x2 - 2xy + y2)
=> A = x2 + 2xy + y2 - x2 + 2xy - y2
=> A = (x2 - x2) + (2xy + 2xy) + (y2 - y2)
=> A = 0 + (2 + 2). xy + 0
=> A = 4xy
b/ B - (x2y-3xy2 +5) = 3x2 + 1 + 4x2y
=> B = (3x2 + 1 + 4x2y) + (x2y-3xy2 +5)
=> B = 3x2 + 1 + 4x2y + x2y - 3xy2 + 5
=> B = (1 + 5) + (4x2y - x2y) + 3x2 - 3xy2
=> B = 6 + 3x2y + 3x2 - 3xy2
D - 9x + 2y3 - 7x3y2 - 4x5y + 1 = 0
=> D = 0 + 9x + 2y3 - 7x3y2 - 4x5y + 1
=> D = 9x + 2y3 - 7x3y2 - 4x5y + 1
P.s: Lần sau bạn đăng 1 câu hỏi/ bài đăng thôi nhé! Và nhớ dùng công thức trực quan!
a) \(A+B+C=\)\(\left(4x^2-5xy+3y^2\right)\)\(+\left(3x^2+2xy+y^2\right)\)\(+\left(2y^2+3xy-x^2\right)\)
\(=4x^2-5xy+3y^2\)\(+3x^2+2xy+y^2\)\(+2y^2+3xy-x^2\)
\(=\left(4x^2+3x^2-x^2\right)+\)\(\left(-5xy+2xy+3xy\right)+\)\(\left(3y^2+y^2+2y^2\right)\)
\(=6x^2+6y^2\)
b)\(B-C-A=\)\(\left(3x^2+2xy+y^2\right)-\left(2y^2+3xy-x^2\right)\)\(\left(\text{4x^2}-5xy+3y^2\right)\)
\(=3x^2+2xy+y^2-2y^2-3xy+x^2-4x^2\)\(+5xy+3y^2\)
\(=\left(-4x^2+3x^2+x^2\right)\)\(+\left(5xy+2xy-3xy\right)\)\(+\left(3y^2+y^2+2y^2\right)\)
\(=4xy+6y^2\)
\(C-A-B=\)\(\left(2y^2+3xy-x^2\right)-\left(4x^2-5xy+3y^2\right)\)\(-\left(3x^2+2xy+y^2\right)\)
\(=2y^2+3xy-x^2-4x^2+5xy-3y^2-3x^2-2xy+y^2\)
\(=\left(-4x^2-3x^2-x^2\right)\)\(+\left(5xy-2xy+3xy\right)\)\(+\left(-3y^2+y^2+2y^2\right)\)
\(=-8x^2+6xy\)
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