câu c (x+3)(x^2-3x+9)-(54+x^3)=x^3+27-54-x^3

=27

a. \(\left(3b+\dfrac{5a}{6}\right)^2\)

= \(9b^2+15ab+\dfrac{25a^2}{36}\)

b. (5x - y)²

= 25x² - 10xy + y²

c. (2a + b - 5)(2a - b + 5)

= 4a² - (b - 5)²

d. \(\left(x^2+\dfrac{2}{5y}\right)\left(x^2-\dfrac{2}{5y}\right)\)

= \(x^4-\dfrac{4}{25y^2}\)

Bài 1:

b: \(x^2-6x+xy-6y\)

\(=x\left(x-6\right)+y\left(x-6\right)\)

\(=\left(x-6\right)\left(x+y\right)\)

c: \(2x^2+2xy-x-y\)

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

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

e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)

Bài 2: Rút gọn biểu thức sau một cách nhanh nhất:

a, A=(6x-2)²+(2-5x)²+2.(6x-2)(2-5x)

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

\(\text{(Hằng đẳng thức số 2)}\)

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

\(=x\)

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

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

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

\(=-4a^2\)

b, 93.107

=(100-7)(100+7)

=100²-7^{2
=10000-49=9951}

c, 2020²-2019²+2018²-2017²+...+2²-1².
=(2²+4²+..+2020²)-(1²+3²+..+2019²)

=(2020.1011.2021)/3 - (1010.(4.1010²-1))/3

= 1375775540 - 1373734330

=2041210

1) \(2xy^3-6x^2+10xy\)

\(=2x.y^3-2x.3x+2x.5y\)

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

\(=2x[y\left(y^2-5\right)-3x]\)

2) \(a^6-a^5-2a^3+2a^2\)

\(=\left(a^6-a^5\right)-\left(2a^3-2a^2\right)\)

\(=\left(a^5.a-a^5.1\right)-\left(2a^2.a-2a^2.1\right)\)

\(=a^5\left(a-1\right)-2a^2\left(a-1\right)\)

\(=\left(a^5-2a^2\right)\left(a-1\right)\)

\(=a^2\left(a^3-2\right)\left(a-1\right)\)

3: \(\left(a+b\right)^3-\left(a-b\right)^3\)

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

\(=2b\left(3a^2+b^2\right)\)

a) ( 6x + 1 )² + ( 6x - 1 )² - 2( 1 + 6x )( 6x - 1 )

=  ( 6x + 1 )² - 2( 1 + 6x )( 6x - 1 ) + ( 6x - 1 )²

= ( 6x + 1 - 6x + 1 )² = 2² = 4

a) A=(4-5x)²-(3+5x)²=(4-5x-3-5x)(4-5x+3+5x)=(-25x+1)1=-25x+1

B=(3x-1)(1+3x)-(3x+1)²=9x²-1-(3x+1)²=9x²-1-(9x²+6x+1)=9x²-1-9x²-6x-1=-6x-2=-2(3x+1)