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a) 2x + 2y - x2 - xy
= 2(x + y) + x(x + y)
= (x + y) (x + 2)
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a)\(2x+2y-x^2-xy=2\left(x+y\right)-x\left(x+y\right)=\left(2-x\right)\left(x+y\right)\)
b)\(\left(x+3\right)^2-\left(2x-5\right)\left(x+3\right)\)
\(=\left(x+3\right)\left[\left(x+3\right)-\left(2x-5\right)\right]\)
\(=\left(x+3\right)\left(8-x\right)\)
c)\(\left(3x+2\right)^2+\left(3x-2\right)^2-2\left(9x^2-4\right)\)
\(=\left(3x+2\right)^2+\left(3x-2\right)^2-2\left(3x-2\right)^2\)
\(=\left(3x+2\right)\left[\left(3x+2\right)-\left(3x-2\right)\right]+\left(3x-2\right)\left[\left(3x-2\right)-\left(3x+2\right)\right]\)
\(=4\left(3x+2\right)-4\left(3x-2\right)\)
\(=4\left(3x+2-3x+2\right)\)
=4.4=16
\(3x^2-5x+2\)
\(=3x^2-3x-2x+2\)
\(=3x\left(x-1\right)-2\left(x-1\right)\)
\(=\left(x-1\right)\left(3x-2\right)\)
Đề sai rồi bạn phải + 2 chứ
\(\left(x+1\right)^2-4\left(x+1\right)y^2+4y^4=\left(x+1-2y^2\right)^2\)
\(\left(x+1\right)^2-4\left(x+1\right)y^2+4y^4\)
\(=\left(x+1-2y^2\right)^2\)
h) \(y\left(y-x\right)^3-x\left(x-y\right)^2+xy\left(x-y\right)=y\left(y-x\right)^3-x\left(y-x\right)^2-xy\left(y-x\right)=\left(y-x\right)\left[y\left(y-x\right)^2-x-xy\right]=\left(y-x\right)\left[y\left(y^2-2xy+x^2\right)-x-xy\right]=\left(y-x\right)\left(y^3-2xy^2+x^2y-x-xy\right)\)
i) \(10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(2b-a\right)^2=10x^2\left(a-2b\right)^2-\left(x^2+2\right)\left(a-2b\right)^2=\left(a-2b\right)^2\left(10x^2-x^2-2\right)=\left(a-2b\right)^2\left(9x^2-2\right)\)
\(\left(x^2+5x\right)^2+10x^2+50x+24\)
\(=\left(x^2+5x\right)^2+10\left(x^2+5x\right)+24\)
\(=\left(x^2+5x\right)^2+4\left(x^2+5x\right)+6\left(x^2+5x\right)+24\)
\(=\left(x^2+5x\right)\left(x^2+5x+4\right)+6\left(x^2+5x+4\right)\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)\)
\(=\left[x^2+x+4x+4\right]\left[x^2+2x+3x+6\right]\)
\(=\left[x\left(x+1\right)+4\left(x+1\right)\right]\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)\)
Chúc bạn học tốt.
(x2 + 5x)2 + 10x2 + 50x + 24
= ( x2 + 5x)2 + 10 ( x2 + 5x) + 24 (1)
Đặt t = x2 + 5x
(1) <=> t2 + 10t + 24
= t2 + 2. t . 5 + 25 -1
= ( t + 5 )2 -1
= ( t + 5 -1 ) ( t + 5 + 1)
= ( t + 4 ) ( t + 6)
thay t = x2 + 5x vào bt trên, ta có
( x2 + 5x + 4) ( x2 + 5x + 6 )
= ( x2 + x + 4x + 4 ) ( x2 + 2x + 3x + 6)
= ( x + 1 ) ( x + 4 ) ( x + 2 ) ( x + 3)
Bài khó quá
4x⁴+4x-3= (2x)²+2(2x)+1-4
=(2x+1)²-2²=(2x+1-2)(2x+1+2)
=(2x-1)(2x+3)
\(=-16x^4y^6-24x^5y^5-9x^6y^4\)
\(=-x^4y^4\left(3x+4y\right)^2\)
x4y4 + x2y2 + 2xy
= ( x3y3 + xy + 2 ) xy
= ( x3y3 + x2y2 - x2y2 - xy + 2xy + 2 ) xy
= [ x2y2 ( xy + 1 ) - xy ( xy + 1 ) + 2 ( xy + 1)] xy
= ( x2y2 - xy + 2 ) ( xy + 1 ) xy
\(\left(2x-1\right)^2=3x^2-4x+5\)
\(\Rightarrow4x^2-4x+1-3x^2+4x-5=0\)
\(\Rightarrow x^2=4\)
\(\Rightarrow x=\pm2\)