Đáp án+Giải thích các bước giải:
`1)`
`x^2+2xy+y^2`
`=x^2+2.x.y+y^2`
`=(x+y)^2`
`x^2+2x+1`
`=x^2 + 2.x.1+1^2`
`=(x+1)^2`
`4x^2+4x+1`
`=(2x)^2 +2.2x.1+1^2`
`=(2x+1)^2`
`x^2+12x+36`
`=x^2+2.x.6+6^2`
`=(x+6)^2`
`2)`
`16x^2+8x+1`
`=(4x)^2+2.4x.1+1^2`
`=(4x+1)^2`
`x^2+x+1/4`
`=x^2+2.x . 1/2 +(1/2)^2`
`=(x+1/2)^2`
`x^2+22x+121`
`=x^2 + 2.x.11+11^2`
`=(x+11)^2`
`x^2+2xy+y^2`
`=x^2+2.x.y+y^2`
`=(x+y)^2`
`3)`
`a^2+4b^2+4ab`
`=a^2 + 2.a.2b +(2b)^2`
`=(a+2b)^2`
`9a^2+4b^2+12ab`
`=(3a)^2+2.3a.2b +(2b)^2`
`=(3a+3b)^2`
`16x^2+24xb+9b^2`
`=(4x)^2+2.4x.3b +(3b)^2`
`=(4x+3b)^2`
`x^2+1/9+2/3x`
`=x^2 + 2. x . 1/3 +(1/3)^2`
`=(x+1/3)^2`
`4)`
`x^2-4x+4`
`=x^2 - 2.x.2+2^2`
`=(x-2)^2`
`x^2-6x+9`
`=x^2-2.x.3+3^2`
`=(x-3)^2`
`25-10a+a^2`
`=5^2 - 2.5.a+a^2`
`=(5-a)^2`
`4+9x^2-12x`
`=2^2 - 2.2.3x +(3x)^2`
`=(2-3x)^2`
`5)`
`x^2-14x +49`
`=x^2-2.x.7+7^2`
`=(x-7)^2`
`x^2-x+1/4`
`=x^2-2.x. 1/2 + (1/2)^2`
`=(x+1/2)^2`
`-x^2-y^2+2xy`
`=-(x^2-2xy+y^2)`
`=-(x-y)^2`
`-4x^2+4xy-y^2`
`=-(4x^2-4xy+y^2)`
`=-[(2x)^2 - 2.2x.y+y^2]`
`=-(2x-y)^2`
`6)`
`25-10a+a^2`
`=5^2 - 2.5.a + a^2`
`=(5-a)^2`
`x^2-18xy+81y^2`
`=x^2 - 2.x.9y +(9y)^2`
`=(x-9y)^2`
`a^2+36b^2-12ab`
`=a^2 - 2.a.6b +(6b)^2`
`=(a-6b)^2`
