Question

因式分解：ax平方+2a平方x+a三次方 16x四次方-8x平方y平方+y四次方 x四次方+8xy三次方

x三次方-5x平方-14x （x平方-5）平方+8（x平方-5）+16 （x平方+4）平方-16x平方

Answer 1

ax² + 2a²x + a³ = a(x² + 2ax + a²) = a(x + a)²
16x⁴- 8x²y² + y⁴= (4x²)² - 2(4x²)y² +(y²)² = (4x² - y²)² = (2x + y)²(2x - y)²
x⁴+xy³ = x(x³ + y³) = x(x + y)(x² -xy +y²)
x³ - 5x² - 14x = x(x² - 5x - 14) = x(x + 2)(x - 7)
(x² - 5)² + 8(x² - 5) + 16 = [(x² - 5) + 4]² = (x² - 1)² = (x + 1)²(x - 1)²
(x² + 4)² - 16x² = [(x² + 4) + 4x][(x² + 4) - 4x] = (x + 2)²(x - 2)²