分解因式:① 1-36b²;② 12x-3y² ;③ 0.49p²-144;④ (2x+y)²-(x+2y)²

问题描述:

分解因式:① 1-36b²;② 12x-3y² ;③ 0.49p²-144;④ (2x+y)²-(x+2y)²

① 1-36b²=﹙1+6b﹚﹙1-6b﹚;
② 12x²-3y²=3﹙4x²-y²﹚=3﹙2x+y﹚﹙2x-y﹚ ;
③ 0.49p²-144=﹙0.7p+12﹚﹙0.7p-12﹚;
④ (2x+y)²-(x+2y)²=[(2x+y)+ (x+2y)][(2x+y)- (x+2y)] =﹙3x+3y﹚﹙x-y﹚=3﹙x+y﹚﹙x-y﹚

① 1-36b²
=(1+6b)(1-6b)
② 12x-3y²
=3(4x-y²)
③ 0.49p²-144
=(0.7p+12)(0.7p-12)
④ (2x+y)²-(x+2y)²
=(2x+y)²-(x+2y)²
=4x²+y²+4xy-x²-4xy-4y²
=3x²-3y²
=3(x²-y²)
=3(x+y)(x-y)