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a) \((3x - 2)(4x + 5)\)
\(\begin{array}{l} = 3x(4x + 5) - 2(4x + 5)\\ = 3x.4x + 5.3x - 2.4x - 2.5\\ = 12{x^2} + 7x - 10\end{array}\)
b) \(({x^2} - 5x + 4)(6x + 1)\)
\(\begin{array}{l} = {x^2}(6x + 1) - 5x(6x + 1) + 4(6x + 1)\\ = {x^2}.6x + 1.{x^2} - 5x.6x - 5x.1 + 4.6x + 4.1\end{array}\)
\( = 6{x^3} - 29{x^2} + 19x + 4\)
a: \(=2x^3:\dfrac{-3}{2}x+4x:\dfrac{3}{2}x-5:\dfrac{3}{2}\)
=-4/3x^2+8/3-10/3
=-4/3x^2-2/3
d: \(\dfrac{3x^3-5x+2}{x-3}=\dfrac{3x^3-9x^2+9x^2-27x+22x-66+68}{x-3}\)
\(=3x^2+9x+22+\dfrac{68}{x-3}\)
a: =3x^3-15x^2+21x
b: =-x^3+6x^2+5x-4x^2-24x-20
=-x^3+2x^2-19x-20
c: =9x^2+15x-3x-5-7x^2-14
=2x^2+12x-19
d: =10x^2-4x+2/3
a: =1/2x^3*x^2-1/2x^3*6x-1/2x^3*10
=1/2x^5-3x^4-5x^3
b: =-3x^2*5x^3+3x^2*4x^2-3x^2*3x+3x^2*3x
=-15x^5+12x^4-9x^3+9x^2
c: \(=3x\cdot5x^2-3x\cdot2x-3x=15x^3-6x^2-3x\)
d: \(=\dfrac{1}{2}x^2y\cdot2x^3-\dfrac{1}{2}x^2y\cdot\dfrac{2}{5}xy^2-\dfrac{1}{2}x^2y=x^5y-\dfrac{1}{5}x^3y^3-\dfrac{1}{2}x^2y\)
a)
\(\begin{array}{l}(3x - 1) + \left[ {(2{x^2} + 5x) + (4 - 3x)} \right] = 3x - 1 + 2{x^2} + 5x + 4 - 3x\\ = 2{x^2}+( 3x +5x- 3x )+ (4 - 1) = 2{x^2} + 5x + 3\end{array}\)
b) Vì A + B = C nên B = C – A
Ta được: B = \(5 - 3{x^2} - 4x - 2\)
\( = - 3{x^2} - 4x + 3\)
Bài 2:
a: \(=2x^4-x^3-10x^2-2x^3+x^2+10x=2x^3-3x^3-9x^2+10x\)
b: \(=\left(x^2-15x\right)\left(x^2-7x+3\right)\)
\(=x^4-7x^3+3x^2-15x^3+105x^2-45x\)
\(=x^4-22x^3+108x^2-45x\)
c: \(=12x^5-18x^4+30x^3-24x^2\)
d: \(=-3x^6+2.4x^5-1.2x^4+1.8x^2\)
* Trả lời:
\(\left(1\right)\) \(-3\left(1-2x\right)-4\left(1+3x\right)=-5x+5\)
\(\Leftrightarrow-3+6x-4-12x=-5x+5\)
\(\Leftrightarrow6x-12x+5x=3+4+5\)
\(\Leftrightarrow x=12\)
\(\left(2\right)\) \(3\left(2x-5\right)-6\left(1-4x\right)=-3x+7\)
\(\Leftrightarrow6x-15-6+24x=-3x+7\)
\(\Leftrightarrow6x+24x+3x=15+6+7\)
\(\Leftrightarrow33x=28\)
\(\Leftrightarrow x=\dfrac{28}{33}\)
\(\left(3\right)\) \(\left(1-3x\right)-2\left(3x-6\right)=-4x-5\)
\(\Leftrightarrow1-3x-6x+12=-4x-5\)
\(\Leftrightarrow-3x-6x+4x=-1-12-5\)
\(\Leftrightarrow-5x=-18\)
\(\Leftrightarrow x=\dfrac{18}{5}\)
\(\left(4\right)\) \(x\left(4x-3\right)-2x\left(2x-1\right)=5x-7\)
\(\Leftrightarrow4x^2-3x-4x^2+2x=5x-7\)
\(\Leftrightarrow-x-5x=-7\)
\(\Leftrightarrow-6x=-7\)
\(\Leftrightarrow x=\dfrac{7}{6}\)
\(\left(5\right)\) \(3x\left(2x-1\right)-6x\left(x+2\right)=-3x+4\)
\(\Leftrightarrow6x^2-3x-6x^2-12x=-3x+4\)
\(\Leftrightarrow-15x+3x=4\)
\(\Leftrightarrow-12x=4\)
\(\Leftrightarrow x=-\dfrac{1}{3}\)
a) \(\begin{array}{l}(4x - 3)(x + 2) = 4x(x + 2) - 3(x + 2)\\ = 4{x^2} + 8x - 3x - 6\end{array}\)
\( = 4{x^2} + 5x - 6\)
b) \((5x + 2)( - {x^2} + 3x + 1)\)
\( = 5x( - {x^2} + 3x + 1) + 2( - {x^2} + 3x + 1)\)
\( = - 5{x^3} + 15{x^2} + 5x - 2{x^2} + 6x + 2\)
\( = - 5{x^3} + 13{x^2} + 11x + 2\)
c) \((2{x^2} - 7x + 4)( - 3{x^2} + 6x + 5)\)
\( = 2{x^2}( - 3{x^2} + 6x + 5) - 7x( - 3{x^2} + 6x + 5) + 4( - 3{x^2} + 6x + 5)\)
\( = 2{x^2}( - 3{x^2}) + 2{x^2}.6x + 2{x^2}.5 + 7x.3{x^2} - 7x.6x - 7x.5 + 4( - 3{x^2}) + 4.6x + 4.5\)
\(= - 6{x^4} + 33{x^3} - 44{x^2} - 11x + 20\)