Bài 2:
1) \(x^2-4=x^2-2^2=\left(x-2\right)\left(x+2\right)\)
2) \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
3) \(4x^2-9=\left(2x\right)^2-3^2=\left(2x+3\right)\left(2x-3\right)\)
4) \(9-25x^2=3^2-\left(5x\right)^2=\left(3-5x\right)\left(3+5x\right)\)
5) \(4x^2-25=\left(2x\right)^2-5^2=\left(2x+5\right)\left(2x-5\right)\)
6) \(9x^2-36=\left(3x\right)^2-6^2=\left(3x-6\right)\left(3x+6\right)\)
7) \(\left(3x\right)^2-y^2=\left(3x-y\right)\left(3x+y\right)\)
8) \(x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)
9) \(\left(2x\right)^2-y^2=\left(2x-y\right)\left(2x+y\right)\)
10) \(\left(3x\right)^2-9y^4=\left(3x\right)^2-\left(3y^2\right)^2=\left(3x-3y^2\right)\left(3x+3y^2\right)\)
Bài 2:
21) \(\left(\dfrac{x}{3}-\dfrac{y}{4}\right)\left(\dfrac{x}{3}+\dfrac{y}{4}\right)=\left(\dfrac{x}{3}\right)^2-\left(\dfrac{y}{4}\right)^2=\dfrac{x^2}{9}-\dfrac{y^2}{16}\)
22) \(\left(\dfrac{x}{y}-\dfrac{2}{3}\right)\left(\dfrac{x}{y}+\dfrac{2}{3}\right)=\left(\dfrac{x}{y}\right)^2-\left(\dfrac{2}{3}\right)^2=\dfrac{x^2}{y^2}-\dfrac{4}{9}\)
23) \(\left(\dfrac{x}{2}+\dfrac{y}{3}\right)\left(\dfrac{x}{2}-\dfrac{y}{3}\right)=\left(\dfrac{x}{2}\right)^2-\left(\dfrac{y}{3}\right)^2=\dfrac{x^2}{4}-\dfrac{y^2}{9}\)
24) \(\left(2x-\dfrac{2}{3}\right)\left(\dfrac{2}{3}+2x\right)=\left(2x-\dfrac{2}{3}\right)\left(2x+\dfrac{2}{3}\right)=\left(2x\right)^2-\left(\dfrac{2}{3}\right)^2=4x^2-\dfrac{4}{9}\)
25) \(\left(2x+\dfrac{3}{5}\right)\left(\dfrac{3}{5}-2x\right)=\left(\dfrac{3}{5}+2x\right)\left(\dfrac{3}{5}-2x\right)=\left(\dfrac{3}{5}\right)^2-\left(2x\right)^2=\dfrac{9}{25}-4x^2\)
26) \(\left(\dfrac{1}{2}x-\dfrac{4}{3}\right)\left(\dfrac{4}{3}+\dfrac{1}{2}x\right)=\left(\dfrac{1}{2}x-\dfrac{4}{3}\right)\left(\dfrac{1}{2}x+\dfrac{4}{3}\right)=\left(\dfrac{1}{2}x\right)^2-\left(\dfrac{4}{3}\right)^2=\dfrac{1}{4}x^2-\dfrac{16}{9}\)
27) \(\left(\dfrac{2}{3}x^2-\dfrac{y}{2}\right)\left(\dfrac{2}{3}x^2+\dfrac{y}{2}\right)=\left(\dfrac{2}{3}x^2\right)^2-\left(\dfrac{y}{2}\right)^2=\dfrac{4}{9}x^4-\dfrac{y^2}{4}\)
28) \(\left(3x-y^2\right)\left(3x+y^2\right)=\left(3x\right)^2-\left(y^2\right)^2=9x^2-y^4\)
29) \(\left(x^2-2y\right)\left(x^2+2y\right)=\left(x^2\right)^2-\left(2y\right)^2=x^4-4y^2\)
30) \(\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x^2\right)^2-\left(y^2\right)^2=x^4-y^4\)
Bài `3`
\(1,\left(2x+1\right)^2+\left(2x-1\right)^2\\ \left[\left(2x\right)^2+4x+1^2\right]+\left[\left(2x\right)^2-4x+1^2\right]\\ =4x^2+4x+1+4x^2-4x+1\\ =8x^2+2\)
\(2,-\left(x+1\right)^2-\left(x-1\right)^2\\ =-\left(x^2+2x+1^2\right)-\left(x^2-2x+1\right)\\ =-x^2-2x-1-x^2+2x-1\\ =-2x^2-2\)
\(3,\left(x+2y\right)^2-\left(x-2y\right)^2\\ =\left[\left(x+2y\right)+\left(x-2y\right)\right]\left[\left(x+2y\right)-\left(x-2y\right)\right]\\ =\left(x+2y+x-2y\right)\left(x+2y-x+2y\right)\\ =2x.4y=8xy\)
\(4,\left(3x+y\right)^2+\left(x-y\right)^2\\ =\left[\left(3x\right)^2+6xy+y^2\right]+\left[\left(x^2-2xy+y^2\right)\right]\\ =6x^2+6xy+y^2+x^2-2xy+y^2\\ =7x^2+4xy+2y^2\)
\(5,-\left(x+5\right)^2-\left(x-3\right)^2\\ =-\left(x^2+10x+5^2\right)-\left(x^2-6x+3^2\right)\\ =-x^2-10x-25-x^2+6x-9\\ =-2x^2+16x-34\)
\(6,\left(3x-2\right)^2-\left(3x-1\right)^2\\ =\left[\left(3x-2\right)+\left(3x-1\right)\right]\left[\left(3x-2\right)-\left(3x-1\right)\right]\\ =\left(3x-2+3x-1\right)\left(3x-2-3x+1\right)\\ =\left(6x-3\right)\left(-1\right)=-6x+3\)
`@ Kidd`
Bài 2:
11) \(16x^2-\left(y^2\right)^2=\left(4x\right)^2-\left(y^2\right)^2=\left(4x-y^2\right)\left(4x+y^2\right)\)
12) \(x^4-\left(3y^2\right)^2=\left(x^2\right)^2-\left(3y^2\right)^2=\left(x^2-3y^2\right)\left(x^2+3y^2\right)\)
13) \(\left(x-1\right)\left(x+1\right)=x^2-1\)
14) \(\left(x+5\right)\left(x-5\right)=x^2-25\)
15) \(\left(x-6\right)\left(6+x\right)=\left(x-6\right)\left(x+6\right)=x^2-36\)
16) \(\left(2x+1\right)\left(2x-1\right)=\left(2x\right)^2-1=4x^2-1\)
17) \(\left(x-2y\right)\left(2y+x\right)=\left(x-2y\right)\left(x+2y\right)=x^2-\left(2y\right)^2=x^2-4y^2\)
18) \(\left(5x-3y\right)\left(3x+5x\right)=\left(5x-3y\right)\left(5x+3y\right)=\left(5x\right)^2-\left(3y\right)^2=25x^2-9y^2\)
19) \(\left(\dfrac{1}{x}-5\right)\left(\dfrac{1}{x}+5\right)=\left(\dfrac{1}{x}\right)^2-5^2=\dfrac{1}{x^2}-25\)
20) \(\left(x-\dfrac{3}{2}\right)\left(x+\dfrac{3}{2}\right)=x^2-\left(\dfrac{3}{2}\right)^2=x^2-\dfrac{9}{4}\)
Bài 2:
1) x2−4=x2−22=(x−2)(x+2)�2−4=�2−22=(�−2)(�+2)
2) 1−4x2=12−(2x)2=(1−2x)(1+2x)1−4�2=12−(2�)2=(1−2�)(1+2�)
3) 4x2−9=(2x)2−32=(2x+3)(2x−3)4�2−9=(2�)2−32=(2�+3)(2�−3)
4) 9−25x2=32−(5x)2=(3−5x)(3+5x)9−25�2=32−(5�)2=(3−5�)(3+5�)
5) 4x2−25=(2x)2−52=(2x+5)(2x−5)4�2−25=(2�)2−52=(2�+5)(2�−5)
6) 9x2−36=(3x)2−62=(3x−6)(3x+6)9�2−36=(3�)2−62=(3�−6)(3�+6)
7) (3x)2−y2=(3x−y)(3x+y)(3�)2−�2=(3�−�)(3�+�)
8) x2−(2y)2=(x−2y)(x+2y)�2−(2�)2=(�−2�)(�+2�)
9) (2x)2−y2=(2x−y)(2x+y)(2�)2−�2=(2�−�)(2�+�)
10) (3x)2−9y4=(3x)2−(3y2)2=(3x−3y2)(3x+3y2)
