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Bài 1:
a) \(x^2+10x+26+y^2+2y=(x^2+10x+25)+(y^2+2y+1)\)
..................................................= \(\left(x+5\right)^2+\left(y+1\right)^2\)
b) \(z^2-6z+5-t^2-4t=(z^2-6t+9)-(t^2+4t+4)\)
............................................= \(\left(z-3\right)^2-\left(t+2\right)^2\)
c) \(x^2-2xy+2y^2+2y+1=(x^2-2xy+y^2)+(y^2+2y+1)\)
..................................................= \(\left(x-y\right)^2+\left(y+1\right)^2\)
d) \(4x^2-12x-y^2+2y+8=\left(4x^2-12x+9\right)-\left(y^2-2y+1\right)\)
.................................................= \(\left(2x-3\right)^2-\left(y-1\right)^2\)
Bài 2:
a) \(\left(x+y+4\right)\left(x+y-4\right)=\left(x+y\right)^2-16\)
b) \(\left(x-y+6\right)\left(x+y-6\right)=x^2-\left(y-6\right)^2\)
c) \(\left(y+2z-3\right)\left(y-2z+3\right)=y^2-\left(2z-3\right)^2\)
d) \(\left(x+2y+3z\right)\left(2y+3z-x\right)=\left(2y+3z\right)^2-x^2\)
\(e,x^2+3x+2=x^2+2x+x+2=x.\left(x+2\right)+x+2=\left(x+1\right).\left(x+2\right)\)
\(f,x^2-7x+12=x^2-3x-4x+12=x.\left(x-3\right)-4.\left(x-3\right)=\left(x-4\right).\left(x-3\right)\)
\(d,x^2-1=x^2-x+x-1=x.\left(x-1\right)+\left(x-1\right)=\left(x+1\right).\left(x-1\right)\)
\(c,x^2+2xy+y^2=x^2+xy+xy+y^2=x.\left(x+y\right)+y.\left(x+y\right)=\left(x+y\right)^2\)
\(b,x^2-2xy+y^2=x^2-xy-xy+y^2=x.\left(x-y\right)-y.\left(x-y\right)=\left(x-y\right)^2\)
Câu a sai đề
a) (x.y)+(x.y)
=> (x.x)+(y.y)
=> x2+y2
b) (x-y)(x-y)
=> (x.x)-(y.y)
=> x2-y2
c) (x+y)(x-y)
=> x2 - y2
d) (x+5).(x-1)
Áp dụng bài c . Ta có :
=> x(x-1) + 5(x-1)
=> x2 - x + 5x - 5
= x2 + 4x - 5
a)(x+y)(x+y)=x^2+2xy+y^2
b)(x-y)(x-y)=x^2-2xy+y^2
c)(x-y)(x-1)=x^2-x-xy+y
d)(x+5)(x-1)+x^2+4x-5