1. \(A=4x^2-\left(x+3\right)\left(x-5\right)+x\)
\(=4x^2-x^2+2x+15+x\)
\(=2x^2+3x+15\)
2. \(B=x^2-2x+5-\left(x-7\right)\left(x+2\right)\)
\(=x^2-2x+5-x^2+5x+14\)
\(=3x+19\)
3. \(C=-5x\left(x-5\right)+\left(x-3\right)\left(x-7\right)\)
\(=-5x^2+25x+x^2-10x+21\)
\(=-4x^2+15x+21\)
4. \(D=\left(a-4\right)\left(a-2\right)-\left(a-1\right)\left(a-3\right)\)
\(=a^2-6a+8-a^2+3a-3\)
\(=-3a+5\)
5. \(E=\left(x^2-5\right)\left(x+3\right)+\left(x+4\right)\left(x-x^2\right)\)
\(=x^3+3x^2-5x+15+x^2-x^3+4x-4x^2\)
\(=-x+15\)
6. \(F=\left(x^2y+y^3\right)\left(x^2+y^2\right)-y\left(x^4+y^4\right)\)
\(=x^4y+x^2y^2+y^3x^2+y^5-yx^4-y^5\)
\(=x^2y^2+y^3x^2=x^2y^2\left(y+1\right)\)
7. \(G=4x\left(x^2-x-1\right)-\left(x^2-2\right)\left(x+3\right)\)
\(=4x^3-4x^2-4x-x^3-3x^2+2x+6\)
\(=3x^3-7x^2-2x+6\)
Tớ làm một nửa trước
8. \(I=\left(x-1\right)\left(x+2\right)-\left(x+5\right)\left(x-2\right)\)
\(=x^2-x-2-x^2-5x+2x+10\)
\(=-4x+8=4\left(2-x\right)\)
9. \(K=\left(-x+5\right)\left(x+3\right)+\left(2x-1\right)\left(x+3\right)\)
\(=-x^2-3x+5x+15+2x^2+6x-x-3\)
\(=x^2+7x+12\) \(=\left(x+3\right)\left(x+4\right)\)
10. \(M=\left(-x-2\right)\left(x+1\right)=\left(x-5\right)\left(-x+1\right)\)
\(=-x^2-x-2x-2+x^2-5x-x+5\)
\(=-9x+3=3\left(1-3x\right)\)
11. \(N=-4x\left(x+3\right)\left(x-7\right)-3x\left(x^2-x+1\right)\)
\(=-4x\left(x^2-4x-21\right)-3x\left(x^2-x+1\right)\)
\(=7x^3+19x^2+81x\)
12. \(P=-3\left(x+4\right)\left(x-7\right)+7\left(x-5\right)\left(x-1\right)\)
\(=-3\left(x^2-3x-28\right)+7\left(x^2-5x+5\right)\)
\(=4x^2-26x+119\)
13. \(Q=\left(2x-3\right)\left(x+4\right)+\left(-x+1\right)\left(x-2\right)\)
\(=2x^2+8x-3x-12-x^2+3x-2\)
\(=x^2+11x-14\)
14. \(R=4x\left(x^2-x+3\right)-\left(x-6\right)\left(x-5\right)\)
\(=4x\left(x^2-x+3\right)-\left(x^2-11x+30\right)\)
\(=4x^3-5x^2+23x-30\)
4: Ta có: \(5x\left(x-3\right)=\left(x-2\right)\left(5x-1\right)-5\)
\(\Leftrightarrow5x^2-15x-5x^2+x+10x-2+5=0\)
\(\Leftrightarrow4x=-3\)
hay \(x=-\dfrac{3}{4}\)
