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\(x^2+5x-6\\ =x^2-x+6x-6\\ =x\left(x-1\right)+6\left(x-1\right)\\ =\left(x+6\right)\left(x-1\right)\\ ---\\ 5x^2+5xy-x-y\\ =x\left(5x-1\right)+y\left(5x-1\right)\\ =\left(5x-1\right)\left(x+y\right)\\ ----\\ 7x-6x^2-2\\ =-6x^2+3x+4x-2\\ =-3x\left(2x-1\right)+2\left(2x-1\right)\\ =\left(2-3x\right)\left(2x-1\right)\)
\(x^2+5x-6=\left(x-1\right)\left(x+6\right)\\ 5x^2+5xy-x-y=\left(5x-1\right)\left(x+y\right)\\ 7x-6x^2-2=\left(3x-2\right)\left(2x-1\right)\)
`@` `\text {Ans}`
`\downarrow`
`x^2 + xy - 2x - 2y`
`= (x^2 - 2x) + (xy - 2y)`
`= x(x - 2) + y(x - 2)`
`= (x + y)(x - 2)`
____
`x^2 - xy - 6x + 6y`
`= (x^2 - 6x) - (xy - 6y)`
`= x(x - 6) - y(x - 6)`
`= (x - y)(x - 6)`
____
`5xy^2 - 5x + y^2 - 1`
`= (5xy^2 + y^2) - (5x + 1)`
`= y^2(5x + 1) - (5x + 1)`
`= (y^2 - 1)(5x + 1)`
`= (y - 1)(y + 1)(5x + 1)`
a: =(x^2+xy)-(2x+2y)
=x(x+y)-2(x+y)
=(x+y)(x-2)
b: =(x^2-xy)-(6x-6y)
=x(x-y)-6(x-y)
=(x-y)(x-6)
c: =5xy^2+y^2-5x-1
=y^2(5x+1)-(5x+1)
=(5x+1)(y^2-1)
=(5x+1)(y+1)(y-1)
\(x^2-6x+9-9y^2=\left(x^2-2\cdot x\cdot3+3^2\right)-\left(3y\right)^2=\left(x-3\right)^2-\left(3y\right)^2\)
\(=\left(x+3y-3\right)\left(x-3y-3\right)\)
\(x^2+5x-2=\left(x^2+2.x.\frac{5}{2}+\frac{25}{4}\right)-\frac{25}{4}-2=\left(x+\frac{5}{2}\right)^2-\frac{33}{4}\)
\(=\left(x+\frac{5}{2}\right)^2-\left(\frac{\sqrt{33}}{2}\right)^2=\left(x+\frac{5}{2}-\frac{\sqrt{33}}{2}\right)\left(x+\frac{5}{2}+\frac{\sqrt{33}}{2}\right)\)
\(=\left(x+\frac{5-\sqrt{33}}{2}\right)\left(x+\frac{5+\sqrt{33}}{2}\right)\)
a: =(x^2-x+1)(x^2+x+1)
b: =x^2-6xy+9y^2=(x-3y)^2
c: =5x(x^2-2xy+y^2)
=5x(x-y)^2
d: =(x-3)^2
e: =(2y-z)(4x+7y)
a)HĐT:(x^2+1-x)(x^2+1+x)
b)=x^2-2.x.3y+(3y)^2
c)=5x(x^2-2xy+y^2)
=5x(x-y)^2
d)x^2-2.3.x+3^2
=(x-3)^2
e)(2y-z)+7y(2y-z)
=(2y-z)(1+7y)
Ta có : x2 - x + 6x - 6
= x(x - 1) + 6(x - 1)
= (x + 6)(x - 1)
b) 5x2 + 5xy - x - y
= 5x(x + y) - (x + y)
= (5x - 1)(x + y)
câu a,b làm như trên. câu c:
c, 7x - 6x2 - 2 = -6x^2 + 7x - 2 = -( 6x^2-3x-4x+2) = -[ 3x ( 2x-1)-2(2x-1)]=-(3x-2)(2x-1)
a: =x^2+2x+3x+6
=(x+2)(x+3)
b: =5x(x+y)-(x+y)
=(x+y)(5x-1)
c: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
\(x^2+5x-6=x^2-6x+x-6=x\left(x-6\right)+\left(x-6\right)=\left(x+1\right)\left(x-6\right)\)
\(5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\)
\(7x-6x^2-2=-6x^2+7x-2=-6\left(x^2-\frac{7}{6}x+\frac{1}{3}\right)=-6\left(x^2-\frac{7}{6}x+\frac{49}{144}-\frac{1}{144}\right)=-6\left[\left(x-\frac{7}{12}\right)^2-\frac{1}{144}\right]\)
1) x2-x+6x-6 = x(x-1)+6(x-1)=(x+6)(x-1)
2) 5x(x+y)-(x+y) =(5x-1)(x+y)
3) -6x2+7x-2 = -6x2+3x+4x-2= -6x(x-\(\frac{1}{2}\)) +4(x-\(\frac{1}{2}\)) =(-3x+2)(2x-1)
a) \(x^2+5x-6\)
\(=x^2-2x+3x-6\\ =\left(x^2-2x\right)+\left(3x-6\right)\\ =x\left(x-2\right)+3\left(x-2\right)\\ =\left(x-2\right)\left(x+3\right)\)
b) \(5x^2+5xy-x-y\)
\(=\left(5x^2+5xy\right)-\left(x+y\right)\\ =5x\left(x+y\right)-\left(x+y\right)\\ =\left(x+y\right)\left(5x+1\right)\)
c)\(7x-6x^2-2\)
\(=3x+4x-6x^2-2\\ =\left(3x-6x^2\right)+\left(4x-2\right)\\ =3x\left(1-2x\right)+2\left(2x-1\right)\\ =3x\left(1-2x\right)-2\left(1-2x\right)\\ =\left(1-2x\right)\left(3x-2\right)\)
\(x^2+5x-6=x^2-x+6x-6=x\left(x-1\right)+6\left(x-1\right)=\left(x+6\right)\left(x-1\right)\)
\(5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)=\left(5x-1\right)\left(x+y\right)\)
\(7x-6x^2-2=3x-6x^2+4x-2=3x\left(1-2x\right)-2\left(1-2x\right)=\left(3x-2\right)\left(1-2x\right)\)
\(a,x^2+5x-6=x^2-x+6x-6\)
\(=x\left(x-1\right)+6\left(x-1\right)=\left(x-1\right)\left(x+6\right)\)
\(b,5x^2+5xy-x-y=5x\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(5x-1\right)\)
\(c,7x-6x^2-2=-6x^2+3x+4x-2\)
\(=-3x\left(2x-1\right)+2\left(2x-1\right)=\left(2x-1\right)\left(2-3x\right)\)