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\(4x^2-\left(x+3\right)\left(x-5\right)+x\)
\(=4x^2-x^2+2x+15+x\)
\(=3x^2+3x+15\)
\(=3\left(x^2+x+5\right)\)
\(=x^6-6x^4+12x^2-8-x^3+x+6x^2-18x\\ =x^6-6x^4-x^3+18x^2-17x-8\)
\(=\left(x-\dfrac{1}{3}\right)\left(\dfrac{4}{3}x+\dfrac{1}{9}-x+\dfrac{1}{3}\right)\\ =\left(x-\dfrac{1}{3}\right)\left(\dfrac{1}{3}x+\dfrac{4}{9}\right)\\ =\dfrac{1}{3}x^2+\dfrac{4}{9}x-\dfrac{1}{9}x-\dfrac{4}{27}\\ =\dfrac{1}{3}x^2+\dfrac{1}{3}x-\dfrac{4}{27}\)
à bài này dễ mà
đầu tiên nhá:không biết,tiếp theo:ko biết.Thế thôi còn lại bạn tự giải
bạn sử dụng hằng đẳng thức nhé .Mình bít nhg lười viết nắm
a: Ta có: \(\left(x+y\right)^2+\left(x-y\right)^2-2x^2\)
\(=x^2+2xy+y^2+x^2-2xy+y^2-2x^2\)
\(=2y^2\)
b: Ta có: \(\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
\(=x^3+3x^2+3x+1-x^3+1-3x^2-3x\)
=2
a) (x-y)2-(x2-2xy)
=y2-2xy+x2-x2+2xy
=y2-(-2xy+2xy)+(x2-x2)
=y2
b)(x-y)2+x2+2xy-(x+y)2
=y2-2xy+x2+x2+2xy-y2-2xy-x2
=(y2-y2)-(2xy+2xy-2xy)+(x2+x2-x2)
=x2-2xy
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) \(\left(x^2-y^2\right)\left(x^2+y^2\right)=\left(x^2\right)^2-\left(y^2\right)^2=x^4-y^4\)
4x2 - ( x + 3 ).( x - 5 ) + x
= 4x^2 - (x -1 + 4)( x - 1 - 4) + x
= (2x)^2 - (x - 1)^2 + 4^2 + x
= (2x - x + 1)(2x + x - 1) + 16 + x
= (x + 1)(x - 1) + 16 + x
= x^2 - 1 + 16 + x
= x^2 + x - 15
4x2 - ( x + 3 ).( x - 5 ) + x
= 4x^2 - (x -1 + 4)( x - 1 - 4) + x
= (2x)^2 - (x - 1)^2 + 4^2 + x
= (2x - x + 1)(2x + x - 1) + 16 + x
= (x + 1)(3x - 1) + 16 + x
= x^2 - x + 3x - 1 + 16 + x
= x^2 + 3x + 16
p/s: cho mk sửa lại nhé, ở trên mk giải sai nha