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\(\left(m-n\right)^6-6\left(m-n\right)^4+12\left(m-n\right)^2-8=\left[\left(m-n\right)^2-2\right]^3\)
\(\dfrac{8}{27}a^3-\dfrac{8}{3}a^2b+8b^2a-8b^3=\left(\dfrac{2}{3}a-2b\right)^3\)
Chúc bạn học tốt !!
bài 1:
a) 4n+4+3n-6<19
<=> 7n-2<19
<=> 7n<21 <=> n< 3
b) n\(^2\) - 6n + 9 - n\(^2\) + 16\(\leq\)43
-6n+25\(\leq\)43
-6n\(\leq\)18
n\(\geq\)-3
h.
n3+ 3n2 -n - 3
= n( n2 -1) + 3( n2 - 1)
= ( n +3)( n2 - 1)
= ( n +3)( n -1)( n +1)
Do n là số nguyên lẻ. Đặt : 2k + 1 = n . Ta có :
( 2k+ 4)2k( 2k +2)
= 2( k + 2)2k . 2( k+ 1)
= 8k( k +1)( k +2)
Do : k ; k+1; k+2 là 3 STN liên tiếp
--> k( k +1).(k+ 2) chia hết cho 6
-->8k( k +1).(k+ 2) chia hết cho 48 với mọi n là số nguyên lẻ
f: \(x^2y^2+2xy+1=\left(xy+1\right)^2\)
g: \(\left(3x-2y\right)^2+2\left(3x-2y\right)+1=\left(3x-2y+1\right)^2\)
h: \(\left(x-3y\right)^2-8\left(x-3y\right)+16=\left(x-3y-4\right)^2\)
i: \(\left(x+y\right)^2+2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y+x-y\right)^2=4x^2\)
1)
a) \(x^2+12x+36=\left(x+6\right)^2\)
b) \(x^2-x+\dfrac{1}{4}=\left(x-\dfrac{1}{2}\right)^2\)
Tick nha
3)
a)\(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=15\)
\(\Leftrightarrow x^3+8-x^3-2x=15\)
\(\Leftrightarrow-2x=15-8\)
\(\Leftrightarrow-2x=7\)
\(\Rightarrow x=\dfrac{-7}{2}\)
b) \(\left(x+3\right)^3-x\left(3x+1\right)^2+\left(2x+1\right)\left(4x^2\right)-5x+1=28\)
\(\Leftrightarrow x^3+9x^2+27x+27-9x^3-6x^2-x+8x^3-10x^2+2x+4x^2-5x+1=28\)
\(\Leftrightarrow0-3x^2+23x+28=28\)
\(\Leftrightarrow-3x^2+23x=0\)
\(\Leftrightarrow-x\left(3x-23\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}-x=0\\3x-23=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{23}{3}\end{matrix}\right.\)
c) \(\left(x^2-1\right)^3-\left(x^4+x^2+1\right)\left(x^2+1\right)=0\)
\(\Leftrightarrow x^6-3x^4+3x^2-1-x^6-2x^4-2x^2-1=0\)
\(\Leftrightarrow-5x^4+x^2-2=0\)
Đặt \(-5t^2+t-2=0\)
\(\Delta=1^2-4\left(-5\right)\left(-2\right)=-39< 0\)
\(\Rightarrow PTVN\)
1.
a)
\(5x\left(x-2y\right)+2\left(2y-x\right)^2\\ =5x\left(x-2y\right)+2\left(x-2y\right)^2\\ =\left(x-2y\right)\left[5x+2\left(x-2y\right)\right]\\ =\left(x-2y\right)\left(5x+2x-4y\right)\\ =\left(x-2y\right)\left(7x-4y\right)\)
b)
\(7x\left(y-4\right)^2-\left(4-y\right)^3\\ =7x\left(4-y\right)^2-\left(4-y\right)^3\\ =\left(4-y\right)^2\left(7x+y-4\right)\)
c)
\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\\ =\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4x-8\right)\\ =\left(4x-8\right)\left(x^2+6-x-7-9\right)\\ =4\left(x-2\right)\left(x^2-x-10\right)\)
b) \(b^3+6b^2+12b+8=b^3+3.b^2.2+3.b.2^2+2^3\\ =\left(b+2\right)^3\)
c) \(\left(m-n\right)^6-6\left(m-n\right)^4+12\left(m-n\right)^2-8\\ =\left[\left(m-n\right)^2\right]^3-3.\left[\left(m-n\right)^2\right]^2.2+3.\left(m-n\right)^2.2^2-2^3\\ =\left[\left(m-n\right)^2-2\right]^3\)