\(=81x^2-\left(z+3y\right)^2\)

\(=\left(9x+z+3y\right)\left(9x-z-3y\right)\)

1, \(x^3+8x^2+17x+10=\left(x^3+x^2\right)+\left(7x^2+7x\right)+\left(10x+10\right)\)

\(=x^2\left(x+1\right)+7x\left(x+1\right)+10\left(x+1\right)\)\(=\left(x+1\right)\left(x^2+7x+10\right)=\left(x+1\right)\left(x+2\right)\left(x+5\right)\)

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

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

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

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

4. \(81x^4+4=\left(9x^2\right)^2+2^2=\left(9x^2+2\right)^2-2.9x^2.2=\left(9x^2+2\right)^2-\left(6x\right)^2\)

\(=\left(9x^2+6x+2\right)\left(9x^2-6x+2\right)\)

a) \(A=\left(x^2+x-2\right)\left(x+7\right)-16\)

\(=x^3+8x^2+5x-14-16\)

\(=x^3+8x^2+5x-30\)

\(=x^3+3x^2+5x^2+15x-10x-30\)

\(=x^2\left(x+3\right)+5x\left(x+3\right)-10\left(x+3\right)\)

\(=\left(x^2+5x-10\right)\left(x+3\right)\)

b) \(A=x^4-2x^3-3x^2+4x+4+x^2-4x+4\)

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

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

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

\(=\left(x-2\right)\left[x^2\left(x+2\right)+2x\left(x+2\right)-2\left(x+2\right)\right]\)

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

c) \(81x^4+4=81x^4+36x^2+4-36x^2\)

\(=\left(9x^2+2\right)^2-\left(6x\right)^2\)

\(=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)

d) \(\left(x^2-3\right)^2+16=x^4-6x^2+25\)

\(=\left(x^4+10x^2+25\right)-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+5\right)\left(x^2+4x+5\right)\)

sửa câu b) xíu nha!

\(A=\left(x-2\right)\left(x^3-2x-4\right)\)

\(=\left(x-2\right)\left[x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\right]\)

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

\(64x^4+y^4\)

\(=\left(8x^2\right)^2+16x^2y^2+y^4-16x^2y^2\)

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

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

\(4x^4+y^4=4x^4+4x^2y^2+y^4-4x^2y^2\)

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

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

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

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

\(=\left(x+2\right)\left[3\left(x-2\right)-1\right]=\left(x+2\right)\left(3x-7\right)\)

x⁴ + 1024 = x⁴ + 64x² + 1024 - 64x²

= (x² + 32)² - (8x)²

= (x² - 8x + 32)(x² + 8x + 32)

Answer:

\(81x^4+4\)

\(=81x^4+36x^2+4-36x^2\)

\(=\left(9x^2+2\right)^2-6x^2\)

\(=\left(9x^2-6x+2\right)\left(9x^2+6x+2\right)\)

Ta có: \(x^4+64\)

\(=\left(x^2\right)^2+2\cdot x^2\cdot8+64-2\cdot x^2\cdot8\)

\(=\left(x^2+8\right)^2-16x^2\)

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