\(\left(x-3\right)\left(x-10\right)\left(x-5\right)\left(x-6\right)-24x^2\)

\(=\left(x^2+30-13x\right)\left(x^2+30-11x\right)-24x^2\)

\(=\left(x^2+30x-12x-x\right)\left(x^2+30x-12x+x\right)-24x^2\)

\(=\left(x^2+30-12x\right)^2-x^2-24x^2\)

\(=\left(x^2-12x+30\right)^2-\left(5x\right)^2\)

\(=\left(x^2-12x+30+5x\right)\left(x^2-12x+30-5x\right)\)

\(=\left(x^2-7x+30\right)\left(x^2-17x+30\right)\)

x¹⁰+x⁸+16x²+24x+16=x²(x⁸+x⁶+16+24/x+16/x²)

24x³ - 3

= 24x³ - 12x² + 12x² - 6x + 6x -3 

= 12x² (2x - 1) + 6x(2x -1) + 3(2x-1)

=(2x-1)(12x² + 6x + 3)

= 3(2x-1)(4x² + 2x + 1) 

a) (x + 2)(x + 4).              b) 2(x + 6)(x + l).

c) 3(3x + 5)(x + l).           d) (6x -7y)(x + y).

Bài 1 :

\(x^2-6x+8=x^2-2x-4x+8=x\left(x-2\right)-4\left(x-2\right)=\left(x-4\right)\left(x-2\right)\)

Bài 2 :

 \(x^8+x^7+1=x^8+x^7+x^6+x^5+x^4+x^3+x^2+x+1-x^6-x^5-x^4-x^3-x^2-x\)

\(=x^6\left(x^2+x+1\right)+x^3\left(x^2+x+1\right)+x^2+x+1-x^4\left(x^2+x+1\right)-x\left(x^2+x+1\right)\)

=\(\left(x^2+x+1\right)\left(x^6+x^3+1-x^4-x\right)\)

Tick đúng nha 

X^2-6+8

\(\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2\)

\(=\left(x^2-13x+30\right)\left(x^2-11x+30\right)-24x^2\)

Đặt \(t=x^2-11x+30\)

\(\Rightarrow\left(x-3\right)\left(x-5\right)\left(x-6\right)\left(x-10\right)-24x^2\)

\(=t.\left(t-2x\right)-24x^2\)

\(=t^2-2xt-24x^2\)

\(=\left(t^2-2xt+x^2\right)-25x^2\)

\(=\left(t-x\right)-\left(5x\right)^2\)

\(=\left(t-6x\right)\left(t+4x\right)\)

\(=\left(x^2-17x+30\right)\left(x^2-7x+30\right)\)

Tham khảo nhé~

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

Trả lời:

2, 8x²y - 8y = 8y ( x² - 1 ) = 8y ( x - 1 )( x + 1 )

3, 24x³ - 3 = 3 ( 8x³ - 1 ) = 3 ( 2x - 1 )( 4x² + 2x + 1 )

4, 4x² - 4y² = ( 2x )² - ( 2y )² = ( 2x - 2y )( 2x + 2y )

5, x⁵ + 27x² = x² ( x³ + 27 ) = x² ( x + 3 )( x² - 3x + 9 )