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

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

(x+4)(x-4)

= x² - 4²

= x² - 16

Áp dụng HĐT: (A-B)(A+B)= A² - B²

(x+4).(x-4)

= x^2  -  4^2

=  x^2  -  16

`(x+4)(x-4)`

`=x^2 - 4^2`

`= x^2-16`

Vận dụng HĐT : `A^2 -B^2=(A-B)(A+B)`

\(F=\left(3x-2\right)^2+\left(3x+2\right)^2+2\left(9x^2-4\right)\\=\left[\left(3x+2\right)^2+2.\left(3x+2\right)\left(3x-2\right)+\left(3x-2\right)^2\right]\\ =\left[\left(3x+2\right)+\left(3x-2\right)\right]^2\\ =\left(6x\right)^2=36x^2\\ Thay.x=-\dfrac{1}{3}.vào.F.thu.gọn:\\ F=36x^2=36.\left(-\dfrac{1}{3}\right)^2=36.\left(\dfrac{1}{9}\right)=4\)

( x - y )⁴ 

= x⁴ - y⁴ 

= (x²)² - (y²)²

=^{\(\orbr{ }\left(x^2\right)-\left(y^2\right)]^2\)}

X²-2XY+Y²

K NHÁ

đ c m 

TRƯƠNG LAN ANH

a) (1-5a)^2 = 1- 10a + 25a^2

b) x^2 - 4  = (x-2)(x+2)

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

d) 4a^2 - 9= (2a - 3)(2a + 3)

Các bạn làm cả công thức hộ mình nha

`(1-5a)^2`

`= 1^2 - 2 . 1 . 5a + (5a)^2`

`= 1 - 10a + 25a^2`

`x^2-4`

`=x^2 -2^2`

`=(x-2)(x+2)`

`1-x^2`

`=1^2 - x^2`

`=(1-x)(1+x)`

`4a^2 - 9`

`=(2a)^2 - 3^2`

`=(2a-3)(2a+3)`

\(1,=x\left(2x+3\right)-\left(2x+3\right)=2x^2+3x-2x-3=2x^2+x-3\\ 2,=\left(2x\right)^2-2.2.x.1+1^2=4x^2-4x+1\)

1. =2x²-2x+3x-3

2. (2x)²-2.2x.1+1²

=4x²-4x+1

(x-2)^3=x³-6x²+12x-8

\(\left(x-2\right)^3=x^3-3\cdot x^2\cdot2+3\cdot x\cdot2^2-2^3\)

\(=x^3-6x^2+12x-8\)

\(\left(x-2\right)^3\)
\(=x^3-3.x^2.2+3.x.2^2-2^3\)
\(=x^3-6x^2+12x-8\)

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

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

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

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

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

9x^2-4=(3x)^2 -2^2=(3x-2)(3x+2)

\(9x^2-4\)

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

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

khai triển hằng đẳng thức đáng nhớ: (xy^2+z)(x^2y^4+z^2-xy^2z+z^2