\(a.\)

\(P\left(x\right)=-x^4+2x^3-2x^2+1\)

\(Q\left(x\right)=x^4+x^3-x^2+3x+1\)

\(b.\)

\(M\left(x\right)=P\left(x\right)+Q\left(x\right)\)

\(=\left(x^4+2x^3-2x^2+1\right)+\left(x^4+x^3-x^2+3x+1\right)\)

\(=3x^3-3x^2+3x+2.\)

\(Bậc\): \(3.\)

tôi làm hết rồi đấy. lần sau nhớ đăng ít thôi. Chia nhỏ ra mà hỏi.

\(8.\left(x+1\right)\left(x^2+3x+9\right)\)

\(=x\left(x^2+3x+9\right)+1\left(x^2+3x+9\right)\)

\(=x^3+3x^2+9x+x^2+3x+9=x^3+4x^2+12x+9.\)

\(9.\left(x-3\right)\left(x^2+3x+9\right)\)

\(=x\left(x^2+3x+9\right)-3\left(x^2+3x+9\right)\)

\(=x^3+3x^2+9x-3x^2-9x-27\)\(=x^3-27.\)

\(10.\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x\left(x^2+2x+4\right)-2\left(x^2+2x+4\right)\)

\(=x^3+2x^2+4x-2x^2-4x-8=x^3-8.\)

\(11.\left(x+4\right)\left(x^2-4x+16\right)\)

\(=x\left(x^2-4x+16\right)+4\left(x^2-4x+16\right)\)

\(=x^3-4x^2+16x+4x^2-16x+64=x^3+64.\)

\(12.\left(x-3y\right)\left(x^2+3xy+9y^2\right)\)

\(=x\left(x^2+3xy+9y^2\right)-3y\left(x^2+3xy+9y^2\right)\)

\(=x^3+3x^2y+9xy^2-3x^2y-9xy^2-27y^3=x^3-27y^3.\)

\(13.\left(x^2-\dfrac{1}{3}\right)\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\)

\(=x^2\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)-\dfrac{1}{3}\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)\)

\(=x^6+\dfrac{1}{3}x^4+\dfrac{1}{9}x^2-\dfrac{1}{3}x^4-\dfrac{1}{9}x^2-\dfrac{1}{27}=x^6-\dfrac{1}{27}.\)

\(4.\left(\dfrac{1}{3}x+2y\right)\cdot\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)\)

\(=\dfrac{1}{3}x\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)+2y\left(\dfrac{1}{9}x^2-\dfrac{2}{3}xy+4y^2\right)\)

\(=\dfrac{4}{3}xy^2-\dfrac{2}{9}x^2y+\dfrac{1}{27}x^3+\dfrac{2}{9}x^2y-\dfrac{4}{3}xy^2+8y^3\)

\(=\dfrac{1}{27}x^3+8y^3.\)

\(1.\left(x+\dfrac{1}{3}\right)^3=\dfrac{\left(3x+1\right)^3}{3^3}=\dfrac{\left(3x+1\right)^3}{27}=\dfrac{27x^3+27x^2+9x+1}{27}\)

\(=x^3+x^2+\dfrac{1}{3}x+\dfrac{1}{27}.\)

\(2.\left(2x+y^2\right)^3=\left(2x\right)^3+3\left(2x\right)^2y^2+3\cdot2x\left(y^2\right)^2+\left(y^2\right)^3\)

\(=8x^3+12x^2y^2+6xy^4+y^6.\)

\(3.\left(\dfrac{1}{2}x^2+\dfrac{1}{3}y\right)^3=\left(\dfrac{1}{2}x^2\right)^3+3\left(\dfrac{1}{2}x^2\right)^2\cdot\dfrac{1}{3}y+3\cdot\dfrac{1}{2}x^2\cdot\left(\dfrac{1}{3}y\right)^2+\left(\dfrac{1}{3}y\right)^3\)

\(=\dfrac{1}{8}x^6+\dfrac{1}{4}x^4y+\dfrac{1}{6}x^2y^2+\dfrac{1}{27}y^3.\)

\(4.\left(3x^2-2y\right)^3\)

\(=\left(3x^2\right)^3-3\left(3x^2\right)^2\cdot2y+3\cdot3x^2\left(2y\right)^2-\left(2y\right)^3\)

\(=27x^6-54x^4y+36x^2y^2-8y^3.\)

\(5.\left(\dfrac{2}{3}x^2-\dfrac{1}{2}y\right)^3\)

\(=\left(\dfrac{2}{3}x^2\right)-3\left(\dfrac{2}{3}x^2\right)^2\cdot\dfrac{1}{2}y+3\cdot\dfrac{2}{3}x^2\cdot\left(\dfrac{1}{2}y\right)^2-\left(\dfrac{1}{2}y\right)^3\)

\(=\dfrac{8}{27}x^6-\dfrac{2}{3}x^4y+\dfrac{1}{2}x^2y^2-\dfrac{1}{8}y^3.\)

\(6.\left(2x+\dfrac{1}{2}\right)^3=\dfrac{\left(4x+1\right)^3}{2^3}=\dfrac{\left(4x+1\right)^3}{8}\)

\(=\dfrac{64x^3+48x^2+12x+1}{8}=8x^3+6x^2+\dfrac{3}{2}x+\dfrac{1}{8}.\)

\(7.\left(x-3\right)^3=x^3-3\cdot x^2\cdot3+3x\cdot3^2-3^3\)

\(=x^3-9x^2+27x-27.\)

câu a bạn sai rồi. Bạn chưa phân tích mà.

\(a.x\left(x-1\right)^2-\left(x+1\right)^3+5x\left(x+2\right)-9\)

\(=x^3-2x^2+x-x^3-3x^2-3x-1+5x^2+10x-9\)

\(=8x-10\)\(=2\cdot4x-2\cdot5=2\left(4x-5\right).\)

\(b.\left(2x-1\right)^3+\left(3x+2\right)^2-8\left(x+1\right)\left(x^2-x+1\right)+3x^2\)

\(=8x^3-12x^2+6x-1+9x^2+12x+4-8x^3-8+3x^2\)

\(=18x-5.\)

\(102^2=10404.\)

\(99^2=9801.\)

\(49\cdot51=2499.\)

What ----> gì

What are you doing.

\(a.\left(y^2x-3ab\right)^2=\left(xy^2-3ab\right)^2=\left(xy^2\right)^2-2xy^2\cdot3ab+\left(3ab\right)^2\)

\(=x^2y^4-6xy^2ab+9a^2b^2.\)