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Ta có: \(2ax^3+6ax^2+6ax+18a\)
\(=2\left[\left(ax^3+3ax^2\right)+\left(3ax+9a\right)\right]\)
\(=2a\left[x^2\left(x+3\right)+3\left(x+3\right)\right]\)
\(=2a\left(x+3\right)\left(x^2+3\right)\)
2ax3 + 6ax2 + 6ax + 18a
= 2a( x3 + 3x2 + 3x + 9 )
= 2a[ ( x3 + 3x2 ) + ( 3x + 9 ) ]
= 2a[ x2( x + 3 ) + 3( x + 3 ) ]
= 2a( x + 3 )( x2 + 3 )
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Sửa ý đầu: \(\left(2a+3\right)x-\left(2a+3\right)y+2a+3\)
\(=\left(2a=3\right)\left(x-y+1\right)\)
\(\left(a-b\right)c+\left(b-a\right)y-a+b\)
\(=\left(a-b\right)c-\left(a-b\right)y-\left(a-b\right)\)
\(=\left(a-b\right)\left(c-y-1\right)\)
\(81a^2+18a+1\)
\(=\left(9a+1\right)^2\)
\(a^3-1\)
\(=\left(a-1\right)\left(a^2+a+1\right)\)
\(a^5-b^5\)
Áp dụng công thức: \(a^{2n+1}-b^{2n+1}=\left(a-b\right)\left(a^{2n}+a^{2n-1}.b+...+b^{2n-1}.a+b^{2n}\right)\)
\(=\left(a-b\right)\left(a^4+a^3b+a^2b^2+ab^3+b^{\text{4}}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: =(5a-a+b)(5a+a-b)
=(4a+b)(5a-b)
b: =(2a-a-b)(2a+a+b)
=(a-b)(3a+b)
c: =(7a-2a+b)(7a+2a-b)
=(5a+b)(9a-b)
d: =(6a-3a+2b)(6a+3a-2b)
=(3a+2b)(9a-2b)
e: =(9a-5a+3b)(9a+5a-3b)
=(4a+3b)(14a-3b)
Lời giải:
$25a^2-(a-b)^2=(5a)^2-(a-b)^2=[5a-(a-b)][5a+(a-b)]=(4a+b)(6a-b)$
$4a^2-(a+b)^2=(2a)^2-(a+b)^2=[2a-(a+b)][2a+(a+b)]=(a-b)(3a+b)$
$49a^2-(2a-b)^2=(7a)^2-(2a-b)^2=[7a-(2a-b)][7a+(2a-b)]=(5a+b)(9a-b)$
$36a^2-(3a-2b)^2=(6a)^2-(3a-2b)^2=[6a-(3a-2b)][6a+(3a-2b)]$
$=(3a+2b)(9a-2b)$
$81a^2-(5a-3b)^2=(9a)^2-(5a-3b)^2=[9a-(5a-3b)][9a+(5a-3b)]$
$=(4a+3b)(14a-3b)$
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a^3+4a^2-7a-10\)
\(=\left(a^3+5a^2\right)-\left(a^2+5a\right)-\left(2a+10\right)\)
\(=a^2\left(a+5\right)-a\left(a+5\right)-2\left(a+5\right)\)
\(=\left(a^2-a-2\right)\left(a+5\right)\)
\(=\left(a^2-2a+a-2\right)\left(a+5\right)\)
\(=\left[a\left(a-2\right)+\left(a-2\right)\right]\left(a+5\right)\)
\(=\left(a+1\right)\left(a-2\right)\left(a+5\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(=7\left(a-b\right)+\left(a-b\right)\left(a+b\right)=\left(a-b\right)\left(7+a+b\right)\)
\(7a-7b+a^2-b^2\)
\(=7\left(a-b\right)+\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a+b+7\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
1: 2a+2b=2(a+b)
2: 2a+4b+6c
=2*a+2*2b+2*3c
=2(a+2b+3c)
3: \(-7a-14ab-21b=-7\left(a+2ab+3b\right)\)
4: \(2ax-2ay+2a=2a\left(x-y+1\right)\)
5: \(=3a\cdot ax-3a\cdot2ay+3a\cdot4=3a\left(ax-2ay+4\right)\)
6: \(=2\cdot2ax-2\cdot ay-2\cdot1=2\cdot\left(2ax-ay-1\right)\)
7: =a^2-(2b)^2
=(a-2b)(a+2b)
8: =(5a)^2-1^2
=(5a-1)(5a+1)
9: =9(16a^2-9)
=9(4a-3)(4a+3)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a^7-a^5+2a^3+2a^2\\ =a^5\left(a^2-1\right)+2a^2\left(a+1\right)\\ =a^5\left(a-1\right)\left(a+1\right)+2a^2\left(a+1\right)\\ =a^2\left(a+1\right)\left(a^4-a^3+2\right)\)
lòn
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