x^2+10 x+25
x^2+14x+49
4x^2+4x+1
9x^2+30x+25
x^2+6xy+9y^2
16x^2+24xy+9y^2
(2x+1)^2+12(2x+1)+36
(x^2+2x)^2+2(x^2+2x)+1
vân dụng hằng đẳng thức (A+B)^phân tích đa thức thành nhân tử
x^2+10 x+25 x^2+14x+49 4x^2+4x+1 9x^2+30x+25 x^2+6xy+9y^2 16x^2+24xy+9y^2 (2x+1)^2+12(2x+1)+36 (x^2+2x)^2+2(x^2+2x)+1 vân dụng hằng đẳng thức (A+B)^ph
By Autumn
`1)x²+10x+25`
`=x²+2.x.5+5²`
`=(x+5)²`
`2)x²+14x+49`
`=x²+2.x.7+7²`
`=(x+7)²`
`3)4x²+4x+1`
`=(2x)²+2.2x.1+1²`
`=(2x+1)²`
`4)9x²+30x+25`
`=(3x)²+2.3x.5+5²`
`=(3x+5)²`
`5)x²+6xy+9y²`
`=x²+2.x.3y+(3y)²`
`=(x+3y)²`
`6)16x²+24xy+9y²`
`=(4x)²+2.4x.3y+(3y)²`
`=(4x+3y)²`
`7)(2x+1)²+12(2x+1)+36`
`=(2x+1)²+2.(2x+1).6+6²`
`=(2x+1+6)²`
`=(2x+7)²`
`8)(x²+2x)²+2(x²+2x)+1`
`=(x²+2x)²+2.(x²+2x).1+1²`
`=(x²+2x+1)²`
`=[(x+1)²]²`
`=(x+1)^4`
Đáp án:
Giải thích các bước giải:
`x^2+10 x+25=(x)^2+2.5x+(5)^2=(x+5)^2`
`x^2+14x+49=(x)^2+2.7x+(7)^2=(x+7)^2`
`4x^2+4x+1=(2x)^2+2.2.1.x+(1)^2=(2x+1)^2`
`9x^2+30x+25=(3x)^2+2.3.5x+(5)^2=(3x+5)^2`
`x^2+6xy+9y^2=(x)^2+2.3xy+(3y)^2=(x+3y)^2`
`16x^2+24xy+9y^2=(4x)^2+2.4.3x+(3y)^2=(4x+3y)^2`
`(2x+1)^2+12(2x+1)+36`
Đặt `2x+1=t`
`t^2+12t+36=(t)^2+2.6t+(6)^2=(t+6)^2=[(2x+1+6)]^2=(2x+7)^2`
`(x^2+2x)^2+2(x^2+2x)+1`
Đặt `x^2+2x=a`
`a^2+2a+1=(a)^2+1.2a+(1)^2=(a+1)^2=[(x^2+2x+1)]^2=[(x+1)^2]^2=(x+1)^4`