x2+2ax+a2 = (x+a)2
x2-2ax+a2 = (x-a)2
x2+6x+9
x2-10x+25
9x2+42x+49
解説動画 ≫
9=32, 6=2×3なので
x2+6x+9 = x2+2×3x+32
= (x+3)2
25=52, -10=-2×5なので
x2-10x+25 = x2-2×5x+52
= (x-5)2
9x2=(3x)2, 49=72, 42x=2×7×(3x)なので
9x2+42x+49 = (3x)2+2×7×(3x)+72
= (3x+7)2
【練習】
x2+12x+36
(x+6)2
x2-18x+81
(x-9)2
4x2+20x+25
(2x+5)2
64x2-16x+1
(8x-1)2