Tìm đa thức A biết
1. A+7x^2y-5xy^2- xy=x^2y+8xy^2-5xy
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\(A=xy\left(x+8y-5\right)-xy\left(7x-5y-1\right)=xy\left[\left(x+8y-5\right)-\left(7x-5y-1\right)\right]=xy\left(-6x+13y-4\right)\)\(Ã=-6x^2y+13xy^2-4xy\)
\(A+B\\ =x^5y^2+7x^2y^4+5xy^3+xy+2+x^2y^4+5xy^3+x^5y^2\\ =\left(x^5y^2+x^5y^2\right)+\left(7x^2y^4+x^2y^4\right)+\left(5xy^3+5xy^3\right)+xy+2\\ =2x^5y^2+8x^2y^4+10xy^3+xy+2\)
`@` `\text {Ans}`
`\downarrow`
`A + B`
`= (x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2) + (x^2y^4 + 5xy^3 + x^5y^2)`
`= x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2 + x^2y^4 + 5xy^3 + x^5y^2`
`= (x^5y^2 + x^5y^2) + (7x^2y^4+ x^2y^4) + (5xy^3+ 5xy^3) + xy + 2`
`= 2x^5y^2 + 8x^2y^4 + 10xy^3 + xy + 2`
P(x)+Q(x)
=3x^2y-2x+5xy^2-7y^2+3xy^2-7y^2-9x^2y-x-5
=8xy^2-14y^2-6x^2y-3x-5
=>Chọn A
`@` `\text {Ans}`
`\downarrow`
`A - B`
`= (x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2) - (x^2y^4 + 5xy^3 + x^5y^2)`
`= x^5y^2 + 7x^2y^4 + 5xy^3 + xy + 2 - x^2y^4 - 5xy^3 - x^5y^2`
`= (x^5y^2 - x^5y^2) + (7x^2y^4 - x^2y^4) + (5xy^3 - 5xy^3) + xy + 2`
`= 6x^2y^4 + xy + 2`
Lời giải:
$A=x^2-8xy+15y^2=x^2-3xy-(5xy-15y^2)$
$=x(x-3y)-5y(x-3y)=(x-3y)(x-5y)$
$B=2x^2-5xy+2y^2=(2x^2-4xy)-(xy-2y^2)$
$=2x(x-2y)-y(x-2y)=(2x-y)(x-2y)$
$C=2x^2-3y^2-xy=(2x^2+2xy)-(3y^2+3xy)$
$=2x(x+y)-3y(y+x)=(x+y)(2x-3y)$
\(A+7x^2y-5xy^2-xy=x^2y+8xy^2-5xy\)
\(\Rightarrow A=\left(x^2y+8xy^2-5xy\right)-\left(7x^2y-5xy^2-xy\right)\)
\(=x^2y+8xy^2-5xy-7x^2y+5xy^2+xy\) \(=\left(x^2y-7x^2y\right)+\left(8xy^2+5xy^2\right)+\left(-5xy+xy\right)\)
\(=-6x^2y+13xy^2-4xy\)
A = (x\(^2\)y + 8xy\(^2\)- 5xy) - (7x\(^2\)y - 5xy\(^2\)- xy)
A = x\(^2\)y + 8xy\(^2\)- 5xy - 7x\(^2\)y + 5xy\(^2\)+ xy
A = (x\(^2\)y -7x\(^2\)y) + (8xy\(^2\)+ 5xy\(^2\)) + (-5xy +xy)
A = -6x\(^2\)y + 13xy\(^2\)- 4xy