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

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

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~

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

\(x^2-24x-8\)

\(x^2-2.12x+144-152\)

\(\Leftrightarrow\left(x-12\right)^2-152\)

\(\Leftrightarrow\left(x-12-\sqrt{152}\right)\left(x-12+\sqrt{152}\right)\)

P/s tham khảo nha

tên của mày nói lên tất cả , ko cần bít đề đúng hay sai , tao cứ đăng thôi :)) 

a, x^4+6x^3+11x^2+6x+1 
= x^4 + 6x^3 + 9x² + 2x² + 6x + 1 
= x^4 + 9x² + 1 + 6x^3 + 2x² + 6x 
= x^4 + 9x² + 1² + 2.x².3x + 2.x².1 + 2.3x.1
= (x² + 3x + 1)²

Mình làm được ý a nên tk 1 tk

bạn tách ra từng ít câu 1 thôi ạ

a: \(=5x\left(xy^2+3x+6y^2\right)\)

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

c: \(=\left(x-3\right)\left(x-4\right)\)

d: \(=x\left(x^2-2xy+y^2-9\right)\)

=x(x-y-3)(x-y+3)

e: \(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)

f: \(=\left(x-4\right)\left(x+3\right)\)

\(4\left(x+5\right)\left(x+6\right)\left(x+10\right)\left(x+12\right)-3x^2\)

\(=4\left[\left(x+5\right)\left(x+12\right)\right]\left[\left(x+6\right)\left(x+10\right)\right]-3x^2\)

\(=4\left(x^2+17x+60\right)\left(x^2+16x+60\right)-3x^2\)

\(=\left(2x^2+34x+120\right)\left(2x^2+32x+60\right)-3x^2\)

\(=\left(2x^2+33x+120\right)^2-x^2-3x^2\)

\(=\left(2x^2+33x+120-2x\right)\left(2x^2+33x+120+2x\right)\)

\(=\left(2x+15\right)\left(x+8\right)\left(2x^2+35x+120\right)\)

\(4\left(x+5\right)\left(x+12\right)\left(x+6\right)\left(x+10\right)-3x^2\)

\(=2\left(x^2+60+17x\right).2\left(x^2+60+16x\right)-3x^2\)

\(=\left(2x^2+120+33x+x\right)\left(2x^2+120+33x-x\right)-3x^2\)

\(=\left(2x^2+120+33x\right)^2-x^2-3x^2\)

\(=\left(2x^2+120+33x\right)^2-4x^2\)

\(=\left(2x^2+120+33x+2x\right)\left(2x^2+120+33x-2x\right)\)

\(=\left(2x^2+35x+120\right)\left(2x^2+31x+120\right)\)

\(=\left(2x^2+35x+120\right)\left(x+8\right)\left(2x+15\right)\)