h, \(27x^3-8=\left(3x-2\right)\left(9x^2+6x+4\right)\)

\(\Rightarrow\left(27x^3-8\right):\left(3x-2\right)\\ =\left(3x-2\right)\left(9x^2+6x+4\right):\left(3x-2\right)\\ =9x^2+6x+4\)

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

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

x^4-5x^2+4=x^4-x^2-(4x^2-4) = x^2(x^2-1)-4(x^2-1)

=(x^2-4)(x^2-1)

=(x-2)(x+2)(x-1)(x+1)                                                            

4. 4x² + 4x + 1 = ( 2x + 1)²

5. \(\dfrac{1}{4}x-\dfrac{2}{3}xy+\dfrac{4}{9}y^2\) \(=\left(\dfrac{1}{2}x\right)^2-2.\dfrac{1}{2}x.\dfrac{2}{3}+\left(\dfrac{2}{3}y\right)^2\)

\(=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)^2\)

6. \(4a^2-\dfrac{4}{3}ab+\dfrac{1}{9}b^2=\left(2a\right)^2-2.2a.\dfrac{1}{3}+\left(\dfrac{1}{3}b\right)^2=\left(2a-\dfrac{1}{3}b\right)^2\)

7.

\(9x^2+4xy+\dfrac{4}{9}y^2-25z^2=\left(3x+\dfrac{2}{3}y\right)^2-\left(5z\right)^2=\left(3x+\dfrac{2}{3}y-5z\right)\left(3x+\dfrac{2}{3}y+5z\right)\)

x² - 6x + 9 = (x-3)²

x² - 2x + 1 - y² = ( x-1)² - y² = ( x-1-y)(x-1+y)

4x² +12xy +9y² = ( 2x+3y)²

\(4.4x^2+4x+1\)

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

\(5.\dfrac{1}{4}x^2-\dfrac{2}{3}xy+\dfrac{4}{9}y^2\)

\(=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)^2\)

\(6.4a^2-\dfrac{4}{3}ab+\dfrac{1}{9}b^2\)

\(=\left(2a-\dfrac{1}{3}b\right)^2\)

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

2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)

3. \(16x^2-8x+1=\left(4x-1\right)^2\)

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

5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)

6. \(a^2-2ab+b^2-x^2=\left(a-b\right)^2-x^2=\left(a-b-x\right)\left(a-b+x\right)\)

7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)

Kết quả nè

1.(x^2-1)^2×(x^2+1)^2

2.(2x-5)^2÷4

3.(4x-1)^2

4.(x+y)^2×(x-y)

5.(1/4x-4/9y)×(1/4x+1/9y)

1.(x^2-1)^2=[(x-1).(x+1]^2

2). (x+5/2)^2

3). {4x-1)^2

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