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\(A=\left(x+y\right)^2-8\left(x+y\right)+2\)
Thay x + y = 5 vào A, ta được:
\(A=5^2-8.5+2=-13\)
Vậy x + y = 5 thì A = -13
1) x2 + xy-8x-8y
= x.(x+y) -8.(x+y)
= (x+y).(x-8)
2) 9x2 -6x + 1 -36y2
=(3x-1)2 -(6y)2
=(3x-1-6y)(3x-1+6y)
3)a2 - b2 -12a+12b
= (a-b)(a+b)-12.(a-b)
=(a-b).(a+b-12)
4)x2 -2xy+8x-16y
=x.(x-2y)+8.(x-2y)
=(x-2y).(x+8)
5) x2 -9y2 +5x+15y
=(x-3y)(x+3y)+5.(x+3y)
= (x+3y).(x-3y+5)
\(1,x^2+xy-8x-8y=x\left(x+y\right)-8\left(x+y\right)=\left(x-8\right)\left(x+y\right)\)\(3,a^2-b^2-12a+12b=\left(a-b\right)\left(a+b\right)-12\left(a-b\right)=\left(a-b\right)\left(a+b-12\right)\)\(4,x^2-2xy+8x-16y=x\left(x-2y\right)+8\left(x-2y\right)=\left(x+8\right)\left(x-2y\right)\)\(5,x^2-9y^2+5x+15y=\left(x-3y\right)\left(x+3y\right)+5\left(x+3y\right)=\left(x+3y\right)\left(x-3y+5\right)\)
x2 + y2 = 8x + y + 8y + x
= ( 8x + x ) + ( 8y + y)
= 9x + 9y
= 9(x+y)
a) 3xy + x +15y +5
= (3xy + x) + (15y + 5)
= x(3y + 1) + 5(3y + 1)
= (3y + 1)(x + 5)
b) 9 - x2 + 2xy - y2
= - [(-9) + (x2 - 2xy + y2 ) ]
= - [( -9) + (x - y)2 ]
= 9 - (x - y)2
= 32 - ( x - y)2
= (3 - x +y)(3 + x - y)
e) x2 - xy - 8x + 8y
= ( x2 - xy ) - (8x - 8y)
= x(x -y) - 8(x-y)
= (x - y)(x - 8)
f) x2 - 6x + 9 - y2
= (x2 - 6x + 9) - y2
= (x - 3)2 - y2
= (x - 3 -y)( x - 3 + y)
h) x2 + 2xy +y2 - yz
= (x2 + 2xy +y2 ) - yz
= (x+y)2 - yz
\(A=\left(x+y\right)^2-8\left(x+y\right)+16-14\\ A=\left(x+y-4\right)^2-14\\ A=\left(5-4\right)^2-14=-13\)
\(A=x^2+2xy+y^2-8x-8y+2\)
\(=\left(x+y\right)^2-8\left(x+y\right)+2\)
\(=5^2-8.5+2\)
\(=-13\)
Vậy \(A=-13\) khi x + y = 5