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\(9\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(3^2\left(x-5\right)^2-\left(x+7\right)^2\)
\(=\)\(\left[3\left(x-5\right)\right]^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15\right)^2-\left(x+7\right)^2\)
\(=\)\(\left(3x-15-x-7\right)\left(3x-15+x+7\right)\)
\(=\)\(\left(2x-22\right)\left(4x-8\right)\)
\(=\)\(2\left(x-11\right).4\left(x-2\right)\)
\(=\)\(8\left(x-11\right)\left(x-2\right)\)
Chúc bạn học tốt ~
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Ta có : (2x + 5)2 - (x - 9)2
= (2x + 5 - x + 9)(2x + 5 + x - 9)
= (x + 14)(3x - 4)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(9\left(x-3\right)^2-4\left(x+1\right)^2\)
\(=\left[3\left(x-3\right)-2\left(x+1\right)\right].\left[3\left(x-3\right)+2\left(x+1\right)\right]\)
\(=\left(3x-9-2x-2\right)\left(3x-9+2x+2\right)\)
\(=\left(x-11\right)\left(5x-7\right)\)
\(9\left(x-3\right)^2-4\left(x+1\right)^2\)
\(=3^2\left(x-3\right)^2-2^2\left(x+1\right)^2\)
\(=\left[3\left(x-3\right)\right]^2-\left[2\left(x+1\right)\right]^2\)
\(=\left[3x-9\right]^2-\left[2x+2\right]^2\)
\(=\left[3x-9-2x-2\right].\left[3x-9+2x+2\right]\)
\(=\left(x-11\right)\left(5x-7\right)\)
Chúc bạn học tốt.
![](https://rs.olm.vn/images/avt/0.png?1311)
\(9\left(x-3\right)^2-4\left(x-1\right)^2=\left(3x-9\right)^2-\left(2x-2\right)^2\)
\(=\left[\left(3x-9\right)-\left(2x-2\right)\right]\left[\left(3x-9\right)+\left(2x-2\right)\right]\)
\(=\left(3x-9-2x+2\right)\left(3x-9+2x-2\right)\)
\(=\left(x-7\right)\left(5x-11\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
x3 +5x2+3x-9
=x3 -x2 +6x2 -6x+9x-9
=x2 (x-1)+6x(x-1) +9(x-1)
=(x-1)(x+6x+9)
=(x-1)(x+3)2
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^5+x+1=x^5-x^2+x^2+x+1=x^2\left(x^3-1\right)+\left(x^2+x+1\right)=x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2+1\right)\)
\(x^{10}+x^5+1=x^{10}-x+x^5-x^2+x^2+x+1=x\left(x^9-1\right)+x^2\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=x\left(x^3-1\right)\left(x^6+x^3+1\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)\left(x^6+x^3+1\right)+x^2\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)\left(x^6+x^3+1\right)+x^2+1\right]\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(9x^2+90x+225-x+1\)
\(=9x^2+89x+226\)