1+12x+36x2
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`a)(x-6)^2-(x+6)^2=12`
`<=>(x-6-x-6)(x-6+x+6)=12`
`<=>-12.2x=12`
`<=>2x=-1`
`<=>x=-1/2`
Vậy `x=-1/2`
`b)36x^2-12x+1=81`
`<=>(6x-1)^2=81`
`<=>(6x-1-9)(6x-1+9)=0`
`<=>(6x-10)(6x+8)=0`
`<=>(3x-5)(3x+4)=0`
`<=>` \(\left[ \begin{array}{l}x=\dfrac53\\x=-\dfrac43\end{array} \right.\)
`c)x^2-4x-12=0`
`<=>x^2-6x+2x-12=0`
`<=>x(x-6)+2(x-6)=0`
`<=>(x-6)(x+2)=0`
`<=>` \(\left[ \begin{array}{l}x=-2\\x=6\end{array} \right.\)
`d)x^2-5x-6=0`
`<=>x^2-6x+x-6=0`
`<=>x(x-6)+x-6=0`
`<=>(x-6)(x+1)=0`
`<=>` \(\left[ \begin{array}{l}x=6\\x=-1\end{array} \right.\)
a) \(=\left(6x\right)^2-2.6x.1+1=\left(6x-1\right)^2\)
b) \(=5xy\left(x^2+2x+1\right)=5xy\left(x+1\right)^2\)
c) \(=\left(3x-y\right)^2-25=\left(3x-y-5\right)\left(3x-y+5\right)\)
d) \(=x\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)
a,x(x+y)-5x-5y
=x(x+y)-5(x+y)
=(x+y)(x-5)
b,3x-5y-6ax+10ay
=(3x-6ax)-(5y-10ay)
=3x(1-2a)-5y(1-2a)
=(1-2a)(3x-5y)
c,a2-6a-b2+6b
=(a2-b2)-(6a-6b)
=(a-b)(a+b)-6(a-b)
=(a-b)(a+b-6)
d,100a2-20a-2b-b2
=(100a2-b2)-(20a+2b)
=(10a-b)(10a+b)-2(10a+b)
=(10a+b)(10a-b-2)
e,36x2-12x+1-b2
=(36x2-12x+1)-b2
=(6x-1)2-b2
=(6x-1-b)(6x-1+b)
f,x2-z2+y2-2xy
=(x2-2xy+y2)-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
Bài 2:
b: \(=\left(x^2+x+4+3x\right)\left(x^2+x+4+5x\right)\)
\(=\left(x^2+4x+4\right)\left(x^2+6x+4\right)\)
\(=\left(x+2\right)^2\cdot\left(x^2+6x+4\right)\)
c: \(=25x^2-49y^2-\left(5x+7y\right)\)
=(5x+7y)(5x-7y-1)
d: \(8x^3-36x^2+54x-27=\left(2x-3\right)^3\)
\(36\times\dfrac{2}{3}=\dfrac{72}{3}=24\\ 280\times\dfrac{3}{5}=\dfrac{840}{5}=168\)
\(\left(1+6x\right)^2\)
\(1+12x+36x^2=\left(6x\right)^2+2.6x.1+1^2=\left(6x+1\right)^2\)