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\(b,=a\left(x+y\right)+2\left(x+y\right)=\left(a+2\right)\left(x+y\right)\\ c,=x\left(x+y\right)-2\left(x+y\right)=\left(x-2\right)\left(x+y\right)\\ d,=5a\left(2x-y\right)-\left(2x-y\right)=\left(5a-1\right)\left(2x-y\right)\)
1) x - y - a(x - y) = (x - y) - a(x - y) = (1 - x)(x - y)
2) a - b + x(a - b) = (a - b) + x(a - b) = (1 + x)(a - b)
3) a(x - y) - x + y = a(x - y) - (x - y) = (a - 1)(x - y)
4) x(a - b) - a + b = x(a - b) - (a - b) = (x - 1)(a - b)
5) ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)
6) ax + ay - bx - by = a(x + y) - b(x + y) = (a - b)(x + y)
7) - 2x - 2y + ax + ay = -2(x + y) + a(x + y) = (a - 2)(x + y)
8) x2 - xy - 2x + 2y = x(x - y) - 2(x - y) = (x - 2)(x - y)
Sorry nha, giờ mình chỉ rảnh làm 8 câu thôi
bn post nhiều nên mình ghi đáp án thôi nhé phần nào sai đề mình cho qua
b)\(\left(x+1\right)\left(xy+1\right)\)
c)\(\left(a+b\right)\left(x+y\right)\)
d)\(\left(x-a\right)\left(x-b\right)\)
e)\(\left(x+y\right)\left(xy-1\right)\)
f)\(\left(a-b\right)\left(x^2+y\right)\)
\(1,ax+ay+bx+by\)
\(=\left(ax+ay\right)+\left(bx+by\right)\)
\(=a\left(x+y\right)+b\left(x+y\right)\)
\(=\left(x+y\right)\left(a+b\right)\)
\(2,ax+ay+2x+2y\)
\(=\left(ax+ay\right)+\left(2x+2y\right)\)
\(=a\left(x+y\right)+2\left(x+y\right)\)
\(=\left(x+y\right)\left(a+2\right)\)
\(3,ax+ay-bx-by\)
\(=\left(ax+ay\right)-\left(bx+by\right)\)
\(=a\left(x+y\right)-b\left(x+y\right)\)
\(=\left(x+y\right)\left(a-b\right)\)
\(4,ax+ay-2x-2y\)
\(=\left(ax+ay\right)-\left(2x+2y\right)\)
\(=a\left(x+y\right)-2\left(x+y\right)\)
\(=\left(x+y\right)\left(a-2\right)\)
ax + ay + bx + by
= a.(x+y) + b.(x+y)
= (x+y).(a+b)
ax + ay + 2x + 2y
= a.(x+y) + 2.(x+y)
= (x+y).(a+2)
ax + ay - bx - by
= a.(x+y) - b.(x+y)
= (x+y).(a-b)
ax + ay - 2x - 2y
= a.(x+y) - 2.(x+y)
= (x+y).(a-2)
Ta có: \(\left(ax+by\right)^2=\left(a^2+b^2\right)\left(x^2+y^2\right)\)
\(\Leftrightarrow a^2x^2+2abxy+b^2y^2=a^2x^2+a^2y^2+x^2b^2+b^2y^2\)
\(\Leftrightarrow2abxy=a^2y^2+x^2b^2\)
\(\Leftrightarrow\left(ay-xb\right)^2=0\)
\(\Leftrightarrow ay=xb\)
hay \(\dfrac{a}{x}=\dfrac{b}{y}\)
\(a,xy+1-x-y\)
\(=\left(xy-y\right)+\left(1-x\right)\)
\(=y\left(x-1\right)- \left(x-1\right)\)
\(=\left(x-1\right)\left(y-1\right)\)
\(b,ax+ay-3x-3y\)
\(=a\left(x+y\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(a-3\right)\)
\(c,x^3-2x^2+2x-4\)
\(=x^2\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2\right)\left(x-2\right)\)
\(d,x^2+ab+ax+bx\)
\(=\left(x^2+ax\right)+\left(ab+bx\right)\)
\(=x\left(a+x\right)+b\left(a+x\right)\)
\(=\left(a+x\right)\left(b+x\right)\)
\(e,16-x^2+2xy-y^2\)
\(=4^2-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
d) ax2 + ay - bx2 - by
= ( ax2 + ay ) - ( bx2 + by )
= a ( x2 + y ) - b ( x2 + y )
= ( x2 + y )( a - b )
c) x2y + xy2 - x - y
= ( x2y + xy2 ) - ( x + y )
= xy ( x + y ) - ( x+ y )
= ( x + y ) ( xy - 1 )
a) \(xy+1-x-y\)
\(=x\left(y-1\right)-\left(y-1\right)\)
\(=\left(y-1\right)\left(x-1\right)\)
b) \(ax+ay-3x-3y\)
\(=a\left(x+y\right)-3\left(x+y\right)\)
\(=\left(x+y\right)\left(a-3\right)\)
c) \(x^3-2x^2+2x-4\)
\(=x^2\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2\right)\)
d) \(x^2+ab+ax+bx\)
\(=x\left(b+x\right)+a\left(b+x\right)\)
\(=\left(b+x\right)\left(a+x\right)\)
e) \(16-x^2+2xy-y^2\)
\(=16-\left(x^2-2xy+y^2\right)\)
\(=4^2-\left(x-y\right)^2\)
\(=\left(4-x+y\right)\left(4+x-y\right)\)
f) \(ax^2+ax-bx^2-bx-a+b\)
\(=\left(ax^2+ax-a\right)-\left(bx^2+bx-b\right)\)
\(=a\left(x^2+x-1\right)-b\left(x^2+x-1\right)\)
\(=\left(x^2+x-1\right)\left(a-b\right)\)
`ab(x-3) -a^2(x-3)`
`=(x-3)(a^2-ab)`
__
`ax+ay+bx+by`
`=a(x+y)+b(x+y)`
`=(x+y)(a+b)`
__
`ax+ay -2x-2y`
`=(ax+ay)-(2x+2y)`
`=a(x+y)-2(x+y)`
`=(x+y)(a-2_`
__
`2x-2y +ax-ay`
`=2(x-y)+a(x-y)`
`=(x-y)(2+a)`
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`10ax -5ay -2x+y`
`= 5a(2x-y) -(2x-y)`
`=(2x-y)(5a-1)`
1: =(x-3)(ab-a^2)
=a(b-a)(x-3)
2: =a(x+y)+b(x+y)
=(x+y)(a+b)
3: =a(x+y)-2(x+y)
=(x+y)(a-2)
4: =2(x-y)+a(x-y)
=(x-y)(a+2)
5: =5a(2x-y)-(2x-y)
=(2x-y)(5a-1)