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10 tháng 8 2021
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Bài tập Tất cả

22 tháng 8 2018

\(1.5x\left(x^2+2x-1\right)-3x^2\left(x-2\right)=5x^3+10x^2-5x-3x^3+6x^2\)

                                                                  \(=2x^3+16x^2-5x\)

                                                                  \(=\left(2x^3-x\right)+\left(16x^2-4x\right)\)

                                                                  \(=x\left(2x^2-1\right)+4x\left(4x-1\right)\left(ĐCCM\right)\)

24 tháng 12 2017

a) (x3 + 8y3) : (2y + x)

= (x + 2y)(x2 - 2xy + 4y2) : (2y + x)

= x2 - 2xy + 4y2

b) (x3 + 3x2y + 3xy2 + y3) : (2x + 2y)

= (x + y)3 : 2(x + y)

= \(\dfrac{\left(x+y\right)^2}{2}\)

c) (6x5y2 - 9x4y3 + 15x3y4) : 3x3y2

= 3x3y2(2x2 - 3xy + 5y2) : 3x3y2

= 2x2 - 3xy + 5y2

1: \(F=\left(\dfrac{-1}{2}-2\right)^3-\left(-\dfrac{1}{2}+3\right)^3+\left(-2+\dfrac{3}{2}\right)^3+\left(-\dfrac{1}{2}+1\right)^2\)

\(=\dfrac{-125}{8}-\dfrac{125}{8}+\dfrac{-1}{8}+\dfrac{1}{4}\)

\(=\dfrac{-251}{8}+\dfrac{1}{4}=\dfrac{-249}{8}\)

2:\(N=\left(-1-1\right)^2-\left(-1+\dfrac{1}{8}\right)+\left(-1+1\right)^3\)

=4+1-1/8

=5-1/8=39/8

22 tháng 7 2017

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. \(x^2-y^2-x+y=\left(x-y\right)\left(x+y\right)-\left(x-y\right)\)

\(=\left(x-y\right)\left(x+y-1\right)\)

11 tháng 7 2017

c)\(x^3+3xy+y^3\)

\(=x^3+y^3+3xy=\left(x+y\right)\left(x^2-xy+y^2\right)+3xy\)

\(=\left(x^2-xy+y^2\right)+3xy\)

\(=x^2-xy+y^2+3xy\)

\(=x^2+2xy+y^2=\left(x+y\right)^2\)

\(=1^2=1\)

11 tháng 7 2017

d) \(x^3-3xy-y^3\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\)

\(=\left(x^2+xy+y^2\right)-3xy\)

\(=x^2-2xy+y^2\)

\(=\left(x-y\right)^2\)

\(=1^2=1\)

@Đoàn Đức Hiếu lm a,b đi nhé