Question

câu 1 x^2 - y^2 -x+y

câu 2 a^3 .x - ab +b-x 

câu 3 x^4 +4x^2 -5

câu 4 x^3 -19x - 30

câu 5 ab ( a-b) +bc (b-c) + ca ( c-a)

câu 6 4a^2 .b^2 -(a^2 +b^2-c^2 )^2

 

Answer 1

1

x²-y²-x+y

=(x-y)(x+y)-(x-y)

=(x-y)(x+y-1)

2

b(1-a)-x(1-a³)

=(1-a)-x(1-a)(1+a+a²)

=(1-a)(1-x-ax-xa²)

3

x⁴+4x²-5

=x⁴+4x²+4-9

=(x²+2)²_3²

=(x²+2-3)(x²+2+3)

=(x²-1)(x²+5)

Answer 2

c6

4a²b²-(a²+b²-c²)²

=(2ab)²-(a²+b²-c²)²

=(2ab-a²-b²+c²)(2ab+a²+b²-c²)

Answer 3

1. \(x^2-y^2-x+y\)

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

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

2. \(a^3x-ab+b-x\)

\(=\left(a^3x-x\right)-\left(ab-b\right)\)

\(=x\left(a^3-1\right)-b\left(a-1\right)\)

\(=x\left(a-1\right)\left(a^2+a+1\right)-b\left(a-1\right)\)

 \(=\left(a-1\right)\left(a^2x+ax+x-b\right)\)

3. \(x^4+4x^2-5\)

\(=x^4+4x^2+4-9\)

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

\(=\left(x^2+5\right)\left(x^2-1\right)\)

 \(=\left(x^2+5\right)\left(x-1\right)\left(x+1\right)\)

4. \(x^3-19x+30\)

\(=x^3-5x^2+5x^2-25x+6x-30\)

\(=x^2\left(x-5\right)+5x\left(x-5\right)+6\left(x-5\right)\)

\(=\left(x^2+5x+6\right)\left(x-5\right)\)

\(=\left(x^2+5x+\frac{25}{4}-\frac{1}{4}\right)\left(x-5\right)\)

\(=\left[\left(x+\frac{5}{2}\right)^2-\left(\frac{1}{2}\right)^2\right]\left(x-5\right)\)

\(=\left(x+3\right)\left(x+2\right)\left(x-5\right)\)

Answer 4

5. \(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)

\(=a^2b-ab^2+b^2c-bc^2+ac^2-a^2c\)

\(=ac^2-abc-a^2c+a^2b-bc^2+b^2c+abc-ab^2\)

\(=ac\left(c-b\right)-a^2\left(c-b\right)-bc\left(c-b\right)+ab\left(c-b\right)\)

\(=\left(ac-a^2-bc+ab\right)\left(c-b\right)\)

\(=\left[a\left(c-a\right)-b\left(c-a\right)\right]\left(c-b\right)\)

\(=\left(a-b\right)\left(c-a\right)\left(c-b\right)\)