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CẢM ƠN NHÌU 
1. 8 - 12x + 6x2 - x3
= 23 - 3.22.x + 3.x2.2 - x3
=(2-x)3
2. 125x3 - 75x2 +15x - 1
=(5x)3 - 3.(5x)2.1 + 3.5x.12 - 13
=(5x - 1)3
3, 4 (sai đề)
5. x3 + 2x2 - 6x - 27
=(x3 - 27) + (2x2 - 6x)
=(x3 - 33) + (2x2 - 6x)
=(x -3)(x2 + 3x + 9) + 2x(x-3)
=(x-3)(x2 + 3x +9 +2x)
=(x-3)(x2 + 5x +9)
6. 12x3 + 4x2- 27x -9
=(12x3 + 4x2) - (27x + 9)
=4x2(3x + 1) - 9(3x +1)
=(3x -1)(4x2 -9)
=(3x-1)(2x-3)(2x+3)
\(1.\)
\(a.\)
\(x^2-2x=x\left(x-2\right)\)
b.
\(3y^3+6xy^2+3x^2y\)
\(=3y\left(y^2+2xy+x^2\right)\)
\(=3y\left(x+y\right)^2\)
\(c.\)
\(x^2-2xy-xy+2y^2\)
\(=x\left(x-2y\right)-y\left(x-2y\right)\)
\(=\left(x-y\right)\left(x-2y\right)\)
\(2.\)
\(a.\)
\(x^2-y^2+5x-5y\)
\(=\left(x-y\right)\left(x+y\right)+5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y+5\right)\)
\(b.\)
\(x^2+4x-y^2+4\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(c.\)
\(x^2-6xy+9y^2-16\)
\(=\left(x^2-6xy+9y^2\right)-4^2\)
\(=\left(x-3\right)^2-4^2\)
\(=\left(x-3-4\right)\left(x-3+4\right)\)
\(=\left(x-7\right)\left(x+1\right)\)
Tương tự câu \(d,e,g\)
\(3.\)
\(a.\)
\(x^3-2x=0\)
\(\Rightarrow x\left(x^2-2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^2-2=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x^2=2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=\pm\sqrt{2}\end{matrix}\right.\)
\(b.\)
\(x\left(x-4\right)+\left(x-4\right)=0\)
\(\Rightarrow\left(x+1\right)\left(x-4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+1=0\\x-4=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-1\\x=4\end{matrix}\right.\)
\(c.\)
\(x\left(x-3\right)+4x-12=0\)
\(\Rightarrow x\left(x-3\right)+3\left(x-3\right)=0\)
\(\Rightarrow\left(x+3\right)\left(x-3\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x+3=0\\x-3=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-3\\x=3\end{matrix}\right.\)
Tương tự \(d,e,g\)
1.=(x-y)(5x+1)
2.=(x+3)(2x+1)
3.=(3x-2y)2(1+1)=2(3x-2y)2
4.bạn chép sai hay sao ý
5.=(2x-3y)2
6. = -(x+y)2
7. = -(a-5)2
1. 5x(x-y)-(y-x)
= 5x(x-y)+(x-y)
= (x-y)(5x+1)
2. 2x(x+3)+(3+x)
= (x+3)(2x+1)
3. (3x-2y)2-(2x-3y)2
= (3x-2y-2x+3y)(3x-2y+2x-3y)
=(x+y)(5x-5y)
=5(x+y)(x-y)
4. 4-(a-b)2
= 22-(a-b)2
= (2-a+b)(2+a-b)
5. 4x2-12xy+9y2
= (2x-3y)2
6. -x2-2xy-y2
= -(x+y)2
7. 10a-a2-25
= -a2+10a-25
= -(a-5)2
\(4x^2-25+\left(2x+7\right)\left(5-2x\right)\)
\(=\left(2x-5\right)\left(2x+5\right)+\left(2x+7\right)\left(5-2x\right)\)
\(=\left(2x-5\right)\left(2x+5\right)-\left(2x-7\right)\left(2x-5\right)\)
\(=\left(2x-5\right)\left(2x+5-2x+7\right)\)
\(=\left(2x-5\right).12\)
Những câu khác làm tương tự
\(a,36x^2-\left(3x-2\right)^2=\left(6x-3x+2\right)\left(6x+3x-2\right)\)
\(=\left(3x+2\right)\left(9x-2\right)\)
phần b,c,d lm tg tự
\(e,16x^2-24xy+9y^2=\left(4x-3y\right)^2\)
4.a) \(2x^2-10x-3x-2x^2-26=0\)
\(-13x-26=0\Rightarrow-13\left(x+2\right)=0\)
\(\Rightarrow x=-2\)
b) \(2\left(x+5\right)-x^2-5x=0\)
\(2x+10-x^2-5x=0\Leftrightarrow-x^2-3x+10=0\)
\(-\left(x^2+3x-10\right)=0\)
\(-\left(x^2-2x+5x-10\right)=-\left(x\left(x-2\right)+5\left(x-2\right)\right)=0\)
\(-\left(x-2\right)\left(x+5\right)=0\)
\(\left\{{}\begin{matrix}x-2=0\\x+5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
c) \(\left(2x-3\right)^2-\left(x+5\right)^2=0\)
\(\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
\(\left(x-8\right)\left(3x+2\right)=0\)
\(\left\{{}\begin{matrix}x-8=0\\3x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)
d) \(x^3+x^2-4x-4=0\)
\(x^2\left(x+1\right)-4\left(x+1\right)=0\)
\(\left(x+1\right)\left(x^2-4\right)=\left(x+1\right)\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x+1=0\\x-2=0\\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-1\\x=2\\x=-2\end{matrix}\right.\)
g) \(\left(x-1\right)\left(2x+3-x\right)=0\)
\(\left(x-1\right)\left(x+3\right)=0\)
\(\Rightarrow\left\{{}\begin{matrix}x-1=0\\x+3=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
h) \(x^2-4x+8-2x+1=x^2-6x+9=0\)
\(\left(x-3\right)^2=0\Rightarrow x=3\)
a) \(=2xy^2\left(x^2+8x+15\right)\)
\(=2xy^2\left[\left(x^2+8x+16\right)-1\right]\)
\(=2xy^2\left[\left(x+4\right)^2-1\right]\)
\(=2xy^2\left(x+4+1\right)\left(x+4-1\right)\)
\(=2xy^2\left(x+5\right)\left(x-3\right)\)
mấy câu sau tự làm nha :*
b,=(x^2-10x+25)-4
=(x-5)^2-2^2
=(x-5-2)(x-5+2)
=(x-7)(x-3)
a, 16(4x+5)2 - 25(2x+2)2
=42 .(4x+5)2 - 52 . (2x+2)2
=(16x+20)2- (10x +10)2
=(16x+20-10x-10)(16x+20+10x+10)
=(6x+10)(26x+30)
=2(3x+5).2.(13x+15)
=4.(3x+5)(13x+15)
b, (x-y+4)2 - (2x +3y -1)2
=(x-y+4-2x-3y+1)(x-y+4+2x+3y-1)
=(-x-4y+5)(3x+2y+3)
c, (x+1)4 - (x-1)4
=[(x+1)2-(x-1)2 ][(x+1)2+(x-1)2]
=(x+1-x+1)(x+1+x-1)[(x+1)2+(x-1)2]
=2.2x[(x+1)2+(x-1)2]
=4x[(x+1)2+(x-1)2]
=4x.(x2+2x+1+x2-2x+1)
=4x.(2x2+2)
=8x.(x2+1)
d,16x2 - 24xy +9y2
= (4x)2 -2.4.x.3y+ (3y)2
=(4x-3y)2
1) \(x^2-16=\left(x-4\right)\left(x+4\right)\)
2)\(4a^{201}\)
3)\(x^2-3=\left(x-\sqrt{3}\right)\left(x+\sqrt{3}\right)\)
4)\(25-9y^2=\left(5-3y\right)\left(5+3y\right)\)
5)\(\left(a+1\right)^2-16=\left(a+1-16\right)\left(a+1+16\right)=\left(a-15\right)\left(a+17\right)\)
6)\(x^2-\left(2+y\right)^2=\left(x-2-y\right)\left(x+2+y\right)\)
7) (a+b)2-(a-b)2
= \(\left(a^2+2ab+b^2\right)-\left(a^2-2ab+b^2\right)=4ab\)
8 ) a^2 + 2ax + x^2
= ( a + x )2
9) x^2 - 4x + 4
= ( x-2)2
10) x^2-6xy+9y^2
= (x - 3y )2
11) x^3+8
= (x+2)( x2 - 2x + 4 )
12) a^3 + 27b^3
= (a + 3b ) ( a2 - 3ab + 9b2 )
13) 27x^3 - 1
= ( 3x -1 ) ( 9x2 + 3x +1)
14) 1/8 - b^3
= ( 1/2 - b ) ( 1/4 + 1/2b + b2)
15) a^3 - (a+b)3
= a3 - ( a3 + 3a2b + 3ab2 + b3)
= - 3a2b - 3ab2- b3= -b (3a2 + 3ab +b2)
16) 4x^2 + 4x + 1
= (2x +1 )2