\(P\left(x\right)+Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)+\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)
\(=-5x^3-\dfrac{1}{3}+8x^4+x^2+x^2-5x-2x^3+x^4-\dfrac{2}{3}\)
\(=-5x+\left(x^2+x^2\right)+\left(-5x^3-2x^3\right)+\left(8x^4+x^4\right)+\left(-\dfrac{1}{3}-\dfrac{2}{3}\right)\)
\(=-5x+2x^2-7x^3+9x^4-1\)
\(P\left(x\right)-Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)-\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)
\(=-5x^3-\dfrac{1}{3}+8x^4+x^2-x^2+5x+2x^3-x^4+\dfrac{2}{3}\)
\(=5x+\left(x^2-x^2\right)+\left(-5x^3+2x^3\right)+\left(8x^4-x^4\right)+\left(-\dfrac{1}{3}+\dfrac{2}{3}\right)\)
\(=5x-3x^3+7x^4+\dfrac{1}{3}\)
Ta có: \(P\left(x\right)+Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)+\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)
\(=-5x^3-\dfrac{1}{3}+8x^4+x^2+x^2-5x-2x^3+x^4-\dfrac{2}{3}\)
\(=\left(-5x^3-2x^3\right)-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(8x^4+x^4\right)+\left(x^2+x^2\right)-5x\)
\(=-7x^3+9x^4+2x^2-5x-1\)
Lại có: \(P\left(x\right)-Q\left(x\right)=\left(-5x^3-\dfrac{1}{3}+8x^4+x^2\right)-\left(x^2-5x-2x^3+x^4-\dfrac{2}{3}\right)\)
\(=-5x^3-\dfrac{1}{3}+8x^4+x^2-x^2+5x+2x^3-x^4+\dfrac{2}{3}\)
\(=\left(-5x^3+2x^3\right)+\left(8x^4-x^4\right)+\left(x^2-x^2\right)+5x-\left(\dfrac{1}{3}-\dfrac{2}{3}\right)\)
\(=-3x^3+7x^4+5x+\dfrac{1}{3}\)
Tuấn Anh Phan Nguyễn Hoang Hung Quan Hung nguyen Nguyễn Huy Tú Ace Legona Hoàng Thị Ngọc Anh Nguyễn Trần Thành Đạt Nguyễn Nhật Minh Nguyễn Phương Trâm Đức Minh và các bn khác nha !!
