Question

证明代数式（x减1)(x加2）（x减3）（x加6）加9乘以x的平方是一个完全平方式

Answer 1

(x-1)(x+2)(x-3)(x+6)+9x²

=[(x-1)(x+6)] * [(x+2)(x-3)] + 9x²

=(x²-6+5x)(x²-6-x)+9x²

=[(x²-6)+5x] * [(x²-6)-x)] + 9x²

=[ (x²-6)²+4x*(x²-6)-5x² ] +9x²

=(x²-6)²+4x*(x²-6)+4x²

=(x²-6)²+2*2x*(x²-6)+(2x)²

=(x²-6+2x)²