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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)\(\left(a-b\right)\left(x^2+y\right)\)
a) \(x^3-2x^2+2x-1^3\)
\(=x\left(x^2-2x+1\right)+x-1\)
\(=x\left(x-1\right)+\left(x-1\right)\)
\(=\left(x+1\right)\left(x-1\right)\)
b) \(x^2y+xy+x+1\)
\(=xy\left(x+1\right)+\left(x+1\right)\)
\(=\left(xy+1\right)\left(x+1\right)\)
c) \(ax+by+ay+bx\)
\(=a\left(x+y\right)+b\left(x+y\right)\)
\(=\left(a+b\right)\left(x+y\right)\)
d) \(x^2-\left(a+b\right)x+ab\)
\(=x^2-ax-bx+ab\)
\(=\left(x^2-ax\right)-\left(bx-ab\right)\)
\(=x\left(x-a\right)-b\left(x-a\right)\)
\(=\left(x-b\right)\left(x-a\right)\)
e) Ko biết làm
f) \(ax^2+ay-bx^2-by\)
\(=\left(ax^2+ay\right)-\left(bx^2+by\right)\)
\(=a\left(x^2+y\right)-b\left(x^2+y\right)\)
\(=\left(a-b\right)\left(x^2+y\right)\)
1: \(=a\left(x+y\right)-4\left(x+y\right)=\left(x+y\right)\left(a-4\right)\)
2: \(=x\left(x+b\right)+a\left(x+b\right)=\left(x+b\right)\left(x+q\right)\)
3: \(=a\left(x+1\right)-b\left(x+1\right)+c\left(x+1\right)\)
\(=\left(x+1\right)\left(a-b+c\right)\)
6: \(=\left(x-y\right)^2-4=\left(x-y-2\right)\left(x-y+2\right)\)
1/ \(\left(x+3\right)^2-\left(2x-5\right)\left(x+3\right).\)
\(=x^2+6x+9-\left(2x^2+6x-5x-15\right)\)
\(=x^2+6x+9-2x^2-6x+5x+15\)
\(=-x^2+5x+24\)
\(=-\left(x^2-5x-24\right)\)
\(=-\left(x^2-8x+3x-24\right)\)
\(=-\left[x\left(x-8\right)+3\left(x-8\right)\right]\)
\(=-\left(x-8\right)\left(x+3\right)\)
2/ \(x^2-xy+x-y\)
\(=\left(x^2+x\right)-\left(xy+y\right)\)
\(=x\left(x+1\right)-y\left(x+1\right)\)
\(=\left(x-y\right)\left(x+1\right)\)
3/ \(x^3+6x^2+9x\)
\(=x\left(x^2+6x+9\right)\)
\(=x\left(x+3\right)^2\)
1,Bạn tự lm
\(2,x^2-xy+x-y=x\left(x-y\right)+\left(x-y\right)=\left(x-1\right)\left(x+1\right)\)
\(3,x^3+6x^2+9x=x\left(x^2+6x+9\right)=x\left(x+3\right)^2\)
\(4,x^2y+xy+x+1=xy\left(x+1\right)+\left(x+1\right)=\left(x+1\right)\left(xy+1\right)\)
\(5,ax+by+ay+bx=\left(ax+ay\right)+\left(by+bx\right)=a\left(x+y\right)+b\left(y+x\right)=\left(x+y\right)\left(a+b\right)\)
\(6,x^2-\left(a+b\right)x+ab=x^2-ax-bx+ab=\left(x^2-bx\right)-\left(ax-ab\right)=x\left(x-b\right)-a\left(x-b\right)=\left(x-b\right)\left(x-a\right)\)
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
\(x^4+x^3+x+1=x^3\left(x+1\right)+\left(x+1\right)=\left(x^3+1\right)\left(x+1\right)=\left(x+1\right)^2\left(x^2-x+1\right)\)
\(x^4-x^3-x+1=\left(x^4-x^3\right)-\left(x-1\right)=\left(x^3-1\right)\left(x-1\right)=\left(x-1\right)^2\left(x^2+x+1\right)\)
\(x^2y+xy^2-\left(x+y\right)=xy\left(x+y\right)-\left(x+y\right)=\left(xy-1\right)\left(x+y\right)\)
\(ax^2+ay-bx^2-by=a\left(x^2+y\right)-b\left(x^2+y\right)=\left(a-b\right)\left(x^2+y\right)\)