把下列格式分解因式,要写过程16-（2a+3b）²（a²+4）²-16a²x²-xy+1/4y²a²x²+16ax+64a⁴-8a²b²+16b⁴9+6（a+b)+(a+b）²写出过程

Answer 1

1、 16 - (2a+3b)² = 4² - (2a+3b)² = [4 - (2a+3b)][4 + (2a+3b)] = (4 - 2a - 3b)(4 + 2a+3b)
2、 (a²+4)² - 16a² = (a²+4)² - (4a)² = [a² + 4 - 4a][a² + 4 +4a] = (a - 2)²(a + 2)²
3、 x² - xy +y²/4 = x² - 2x(y/2) +(y/2)² = (x - y/2)²
4、 a²x² + 16ax + 64 = (ax)² + 2(ax)*8 + 8² = (ax + 8)²
5、 a⁴ - 8*a²b² + 16b⁴= (a²)² - 2*(a²)(4b²)+ (4b²)² = (a² - 4b²)² = [(a - 2b)²(a + 2b)²]
6、 9 + 6(a+b) + (a+b)² = 3² + 2*3*(a+b) + (a+b)² = (3 + a + b)²