a) \(P\left(x\right)-x\left(x+5\right)-\left(2x-3\right)+x^2\left(3x-2\right)\)

\(P\left(x\right)=-x^2-5x-2x+3+3x^3-2x^2\)

\(P\left(x\right)=3x^3+\left(-x^2-2x^2\right)-\left(5x+2x\right)+3\)

\(P\left(x\right)=3x^3-3x^2-7x+3\)

b) \(Q\left(x\right)=2x\left(x+1\right)+3x\left(5-x\right)-7\left(x-5\right)\)

\(Q\left(x\right)=2x^2+2x+15x-3x^2-7x+35\)

\(Q\left(x\right)=-x^2+10x+35\)

a: P(x)=-x^2-5x-2x+3+3x^3-2x^2

=3x^3-3x^2-7x+3

b: Q(x)=2x^2+2x+15x-3x^2-7x+35

=-x^2+10x+35

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

\(=2x^2-4x+5x+15+3x+3=2x^2+4x+18.\)

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

\(=5x^2-2x-2+3x^2-6x+5=8x^2-8x+3.\)

a)\(P\left(x\right)=x^4+3\)

b)\(Q\left(x\right)=-x^3-2x^2-14x-1\)

(6x+1)(2x-5)=12x²-30x+2x-5=12x²-28x-5

(2x+5)²-2x(2x+8)=4x²+20x+25-4x²-16x=4x+25

(3x-5)(2x-1)-(2x+3)(3x+7)+30x=6x²-3x-10x+5=6x²-13x+5

(X-1)²-(x+1)(x-1)=x²-2x+1-x²+1=-2x+2

(3x+2)(9x²-6x+4)-(3+x)(x-3)=27x³+8+9-x²=27x³-x²+17

1. Thu gọn biểu thức - Hoc24 làm rồi mà bạn?

1.

a) \(=x^2-6x+9+3x^2-15x=4x^2-21x+9\)

b) \(=9x^2+12x+4-x^2+9=8x^2+12x+13\)

2.

a) \(\Leftrightarrow x^2+8x+16-x^2+4-5=0\\ \Leftrightarrow8x=-15\\ \Leftrightarrow x=-\dfrac{15}{8}\)

b) \(\Leftrightarrow9x^2-6x+1-8x^2+12x-2x+3-5-x^2=0\\ \Leftrightarrow4x=1\\ \Leftrightarrow x=\dfrac{1}{4}\)

1,a,=x2−6x+8+3x2−15x=4x2−21x+8b,=9x2+12x+4−x2+9=8x2+12x+132,a,⇔x2+8x+16−x2+4=5⇔8x=−15⇔x=−158b,⇔9x2−6x+1−8x2−2x+12x+3−x2=5⇔4x=1⇔x=14

a: =18x^3y^2-12x^3y^3+6x^2y^2

b: (-3x+2)(5x^2-1/3x+4)

=-12x^3+x^2-12x+10x^2-2/3x+8

=-12x^3+11x^2-38/3x+8

c: =x^2-x-2+3x-x^2

=2x-2

d: =4x^2+12x+9-4x^2+25-(x-1)(x^2+12)

=12x+34-x^3-12x+x^2+12

=-x^3+x^2+46

a) \(P_{\left(x\right)}=3x^2+2x^3+2x+5-x^2-x-5\)

\(P_{\left(x\right)}=2x^3+2x^2+x\)

\(Q_{\left(x\right)}=x^3-2x-2+3x-x^2+1\)

\(Q_{\left(x\right)}=x^3-x^2+x-1\)

b) ta có: \(P_{\left(x\right)}+Q_{\left(x\right)}=\left(2x^3+2x^2+x\right)+\left(x^3-x^2+x-1\right)\)

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

                                      \(=3x^3+x^2+2x-1\)

ta có: \(P_{\left(x\right)}-Q_{\left(x\right)}=\left(2x^3+2x^2+x\right)-\left(x^3-x^2+x-1\right)\)

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

                                 \(=x^3+3x^2+1\)

\(M\left(x\right)=2x\left(x-3\right)-5\left(x-2\right)+3x^2\)

\(=2x^2-6x-5x+10+3x^2\)

\(=5x^2-11x+10\)

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

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

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

\(M\left(x\right)-N\left(x\right)-x^2\left(x+6\right)\)

\(=5x^2-11x+10-\left(2x^3-4x^2-3x+4\right)-x^2\left(x+6\right)\)

\(=5x^2-11x+10-2x^3+4x^2+3x-4-x^3-6x^2\)

\(=-3x^3+3x^2-8x+6\)