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\(A=x^3+12x^2+48x+64=\left(x+4\right)^3\)
\(B=x^3-6x^2+12x-8=\left(x-2\right)^3\)
\(D=\left(x+2y+z\right)\left(x+2y-z\right)=\left(x+2y\right)^2-\left(z\right)^2\)
\(E=\left(2x-1\right)\left(4x^2+2x+1\right)=8x^3-1\)
\(C=\left(2x+y^2\right)^3=\left(2x\right)^2+3\left(2x\right)^2y^2+3.2x\left(y^2\right)^3+\left(y^2\right)^3\)
c: \(5\left(a+b\right)+x\left(a+b\right)\)
=(a+b)(x+5)
d: \(\left(a-b\right)^2-\left(b-a\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\)
=(a-b)(a-b+1)
e: \(=\left(12x^2+6x\right)\left(y+z+y-z\right)\)
\(=2y\cdot6x\cdot\left(2x+1\right)=12xy\left(2x+1\right)\)
Giải:
3x2- 9x2+12x2y2 = 3x2(1-3+4y2)
x2yz+xy2z+xyz2 = xyz(x+y+z)
ax+ay = a(x+y)
2x+4y2 = 2(x+2y2)
2x2+6x = 2x(x+3)
5x10-10x6 = 5x6(x4-2)
bx2-by = b(x2-y)
10xy2 -10x2y3 = 10xy2(1-xy2)
64xy-96x2y+48x3y-8x4y = 8xy(8-12x+6x2-x2)
17x3y-34x2y2 = 17x2y(x-2y2)
12x2-18xy2-30y3 = 6(2x2-3xy2-5y3)
7x+7y = 7(x+y)
a2x+a2y = a2(x+y)
36x6y4-27x5y5 = 9x5y4(4x-3y)
6x4-9x3 = 3x3(2x-3)
5x2y-15x2y2 = 5x2y(1-3y)
abc2+a2bc-ab2c = abc(c+a-b)
Chúc bạn học tốt!
2.
a) . -x3 + 3x2 - 3x + 1
=13-3.12x+3.1.x2-x3
=(1-x)3
b)8- 12x + 6x2 - x3
=23-3.22.x+3.2.x2-x3
=(2-x)3
3.
a) x3 + 12x2 + 48x + 64 tại x = 6
=x3+3.x2.4+3x4+432
=(x+4)3thay x=6 ta được :
(6+4)3=103=1000
b) x3 - 6x2 + 12x - 8 tại x= 22
=x3-3.x2.2+3.x.22 -23
=(x-2)3 thay x=22 ta đc:
=(22-2)3=203=8000
a)\(\left(2x-y\right)[\left(2x\right)^2-2.2x.y+y^2]\)
\(=\left(2x-y\right)^3\)
b)\(2x^2-3xy+5y^2\)
c)\(2x^3-10x^2-11x^2+55x+12x-60\)
\(=2x^2\left(x-5\right)-11x\left(x-5\right)+12\left(x-5\right)\)
\(=\left(x+5\right)\left(2x^2-11x+12\right)\)
\(\Leftrightarrow(2x^3-21x^2+67x-60)/\left(x-5\right)=2x^2-11x+12\)
\(3x^3y^2-6x^2y^3+9x^2y^2=3x^2y^2\left(x-2y+3\right)\)
\(5x^2y^3-25x^3y^4+10x^3y^3=5x^2y^3\left(1-5xy+2x\right)\)
\(12x^2y-18xy^2-3xy^2=3xy\left(4x-6y-y\right)\)
\(5\left(x-y\right)-y\left(x-y\right)=\left(x-y\right)\left(5-y\right)\)
\(y\left(x-z\right)+7\left(z-x\right)=y\left(x-z\right)-7\left(x-z\right)=\left(x-z\right)\left(y-7\right)\)
\(27x^2\left(y-1\right)-9x^3\left(1-y\right)=27x^2\left(y-1\right)+9x^3\left(y-1\right)=9x^2\left(y-1\right)\left(3-x\right)\)
2 .tìm x
a , x ( x + 2 ) = 0
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
b, x ( x-5 )= 5 -x
<=> x ( x-5 ) + x - 5 = 0
<=> x (x-5) + ( x-5)= 0
<=> (x-5)(x+1 )=0
\(\Leftrightarrow\left\{{}\begin{matrix}x-5=0\\x+1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=5\\x=-1\end{matrix}\right.\)
c) ( x + 1 ) ( 6x2 + 2x ) + ( x - 1 ) ( 6x2 + 2x ) = 0
\(\Leftrightarrow\) ( 6x2 + 2x ) \([\)(x+1)(x-1)\(]\)=0
\(\Leftrightarrow\) \(\left\{{}\begin{matrix}2x\left(3x+1\right)=0\\x^{2^{ }}-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x=0\\3x+1=0\\x^2-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=0\\x=\frac{-1}{3}\\x=1\end{matrix}\right.\)
1 ,a) 2a ( x - y ) - ( y - x ) = 2ax - 2ay - y + x
= x ( 2a + 1 ) - y ( 2a + 1 )
= ( 2a + 1 ) ( x - y )
b) a2 ( x - y ) - ( y - x ) = a2x - a2y - y + x
= x ( a2+ 1 ) - y ( a2 +1 )
= ( a2+1 ) - (x-y )
c) x ( x - y ) + y ( y - x ) - 3 ( x - y ) = x 2 - xy -+ y 2 - xy - 3x + 3y
= x2 - 2xy + y2 -3x + 3y
= (x-y)2 -3 ( x - y )
= ( x-y ) ( x-y+3)