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a)x3-7x+6
=x3+0x2-7x+6
=x3-x2+x2-x-6x+6
=(x3-x2)+(x2-x)-(6x-6)
=x2(x-1)+x(x-1)-6(x-1)
=(x-1)(x2+x-6)
=(x-1)(x2-2x+3x-6)
=(x-1)[x(x-2)+3(x-2)]
=(x-1)(x+3)(x-2)
bạn hỏi từng câu 1 lần thôi cũng đc hỏi 1 lần 17 câu thì thánh nào vô kiên nhẫn trả lời hết đc ^^
2: \(=a^2\left(a+3\right)+4\left(a+3\right)=\left(a+3\right)\left(a^2+4\right)\)
3: \(=\left(2a-1\right)^2-4b^2\)
\(=\left(2a-1-2b\right)\left(2a-1+2b\right)\)
4: \(=-\left(x^2+x-2\right)=-\left(x+2\right)\left(x-1\right)\)
5: \(=7\left(x^2-2xy^2+y^4\right)=7\left(x-y^2\right)^2\)
6: \(=\left(x+2\right)^2-y^2=\left(x+2+y\right)\left(x+2-y\right)\)
1/ \(x^2+2xy+y^2-x-y-12=\left(x+y\right)^2+6\left(x+y\right)+9-7\left(x+y\right)-21\)
\(=\left(x+y+3\right)^2-7\left(x+y+3\right)=\left(x+y+3\right)\left(x+y-4\right)\)
2/ \(4x^4-32x^2+1=\left(4x^4+4x^2+1\right)-36x^2\)
\(=\left(2x^2+1\right)^2-36x^2=\left(2x^2-6x+1\right)\left(2x^2+6x+1\right)\)
3/ \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2=2x^4-2x^3-2x+2\)
\(=2\left(x-1\right)^2\left(x^2+x+1\right)\)
Còn lại tự làm nhé
1: \(=\dfrac{x^2\cdot4xy^2}{x^2}=4xy^2\)
2: \(=\dfrac{3x\left(x-2\right)}{-\left(x-2\right)}=-3x\)
3: \(=\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{x^2+2x+4}=x-2\)
6: \(\dfrac{5\left(x-y\right)^4-3\left(x-y\right)^3+4\left(x-y\right)^2}{\left(x-y\right)^2}=5\left(x-y\right)^2-3\left(x-y\right)+4\)
1 ) x3 - 2x2 + x
= x( x2 - 2x + 1 )
= x ( x-1)2
2) 4x3 - 25x
= x ( 4x2 - 25)
= x( 2x-5) ( 2x +5)
11) \(x^2-y^2-4x+4\)
\(=\left(x^2-4x+4\right)-y^2\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-y-2\right)\left(x+y-2\right)\)
13) \(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
1. \(125x^3+y^6=\left(5x\right)^3+\left(y^2\right)^3\)
\(=\left(5x+y^2\right)\left[\left(5x\right)^2-5x.y^2+\left(y^2\right)^2\right]\)
\(=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)
2. \(4x\left(x-2y\right)+8y\left(2y-x\right)\)
\(=4x\left(x-2y\right)-8y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(4x-8y\right)\)
3. \(25\left(x-y\right)^2-16\left(x+y\right)^2\)
\(=\left[5\left(x-y\right)\right]^2-\left[4\left(x+y\right)\right]^2\)
\(=\left[5\left(x-y\right)-4\left(x+y\right)\right]\left[5\left(x-y\right)+4\left(x+y\right)\right]\)
\(=\left(5x-5y-4x-4y\right)\left(5x-5y+4x+4y\right)\)
\(=\left(x-9y\right)\left(9x-y\right)\)
4. \(x^4-x^3-x^2+1\)
\(=x^3\left(x-1\right)-\left(x^2-1\right)\)
\(=x^3\left(x-1\right)-\left(x-1\right)\left(x+1\right)\)
\(=\left(x-1\right)\left(x^3-x-1\right)\)
5. \(a^3x-ab+b-x\)
\(=a^3x-x-ab+b\)
\(=x\left(a^3-1\right)-b\left(a-1\right)\)
\(=x\left(a-1\right)\left(a^2+a+1\right)-b\left(a-1\right)\)
\(=\left(a-1\right)\left[x\left(a^2+a+1\right)-b\right]\)
6. \(x^3-64=x^3-4^3\)
\(=\left(x-4\right)\left(x^2+4x+16\right)\)
7. \(0,125\left(a+1\right)^3-1\)
\(=\left[0,5\left(a+1\right)\right]^3-1^3\)
\(=\left[0,5\left(a+1\right)-1\right]\left\{\left[0,5\left(a+1\right)\right]^2+\left[0,5\left(a+1\right).1\right]+1^2\right\}\)
\(=\left[0,5\left(a+1-2\right)\right]\left[0,25a^2+0,5a+0,25+0,5a+0,5+1\right]\)
\(=\left[0,5\left(a-1\right)\right]\left(0,25a^2+a+1,75\right)\)
8. \(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left[3\left(x+5\right)\right]^2-\left(x-7\right)^2\)
\(=\left(3x+15-x+7\right)\left(3x+15+x-7\right)\)
\(=\left(2x+22\right)\left(4x+8\right)\)
9. \(49\left(y-4\right)^2-9\left(y+2\right)^2\)
\(=\left[7\left(y-4\right)\right]^2-\left[3\left(y+2\right)\right]^2\)
\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)
\(=\left(4y-34\right)\left(10y-22\right)\)
10. \(x^2y+xy^2-x-y=xy\left(x+y\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(xy-1\right)\)
11. \(x^3+3x^2+3x+1-27z^3\)
\(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
12. \(x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-1\right)\)
Bài 1:
a: \(6x^2-11x+3\)
\(=6x^2-9x-2x+3\)
\(=3x\left(2x-3\right)-\left(2x-3\right)\)
\(=\left(2x-3\right)\left(3x-1\right)\)
b: \(2x^2+3x-27\)
\(=2x^2+9x-6x-27\)
\(=x\left(2x+9\right)-3\left(2x+9\right)\)
\(=\left(2x+9\right)\left(x-3\right)\)
c: \(x^2-10x+24\)
\(=x^2-4x-6x+24\)
\(=x\left(x-4\right)-6\left(x-4\right)\)
\(=\left(x-4\right)\left(x-6\right)\)
d: \(49x^2+28x-5\)
\(=49x^2+28x+4-9\)
\(=\left(7x+2\right)^2-9\)
\(=\left(7x-1\right)\left(7x+5\right)\)
e: \(2x^2-5xy-3y^2\)
\(=2x^2-6xy+xy-3y^2\)
\(=2x\left(x-3y\right)+y\left(x-3y\right)\)
\(=\left(x-3y\right)\left(2x+y\right)\)
6) Ta có: \(x^2+2xy+y^2-x-y-12\)
\(=\left(x+y\right)^2-\left(x+y\right)-12\)
\(=\left(x+y-4\right)\left(x+y+3\right)\)
7) Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24\)
\(=\left(x^2+7x\right)^2+22\left(x^2+7x\right)+96\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
8) Ta có: \(4x^4-32x^2+1\)
\(=4x^4+12x^3+2x^2-12x^3-36x^2-6x+2x^2+6x+1\)
\(=2x^2\left(2x^2+6x+1\right)-6x\left(2x^2+6x+1\right)+\left(2x^2+6x+1\right)\)
\(=\left(2x^2+6x+1\right)\left(2x^2-6x+1\right)\)
9) Ta có: \(3\left(x^4+x^2+1\right)-\left(x^2+x+1\right)^2\)
\(=3\left[x^4+2x^2+1-x^2\right]-\left(x^2+x+1\right)^2\)
\(=3\left(x^2-x+1\right)\left(x^2+x+1\right)-\left(x^2+x+1\right)^2\)
\(=\left(x^2+x+1\right)\left(3x^2-3x+3-x^2-x-1\right)\)
\(=\left(x^2+x+1\right)\left(2x^2-4x+2\right)\)
\(=2\left(x-1\right)^2\cdot\left(x^2+x+1\right)\)