thực hiện các phép tính sau:
a) x(x^2+4x+5)-x^2(x+4)
b) (x-2)^2+(3-x)(x-1)
c) (x+2)^3-x(x^2+6x+12)
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\(a,=12x^2-4x-6x-2-x-3=12x^2-11x-5\\ b,=12x^2-9x-12x^2-4x+5=5-13x\\ c,=12x^3-4x^2-12x^3-12x^2+7x-3=-16x^2+7x-3\\ d,=\left(x^2-4\right)\left(x^2+4\right)=x^4-16\)
Đáp án:
a.3x³−5x²+7xa.3x³−5x²+7x
b.−4x²y−10x²y+2xyb.−4x²y−10x²y+2xy
c.−x³+2x²+29x+20c.−x³+2x²+29x+20
d.2x⁴−3x³+2x²+3x−4d.2x⁴−3x³+2x²+3x−4
e.x²−4y²e.x²−4y²
h.2x²−6x+13h.2x²−6x+13
g.3xy⁴
b: \(\frac{-20x}{3y^2}:\frac{-4x^3}{5y}=\frac{-20x}{3y^2}\cdot\frac{5y}{-4x^3}=\frac{20\cdot5\cdot xy}{3y^2\cdot4x^3}=\frac{100xy}{12x^3y^2}=\frac{25}{3x^2y}\)
c: \(\frac{4x+12}{\left(x+4\right)^2}:\frac{3\left(x+3\right)}{x+4}\)
\(=\frac{4\left(x+3\right)}{\left(x+4\right)^2}\cdot\frac{x+4}{3\cdot\left(x+3\right)}\)
\(=\frac{4}{3\left(x+4\right)}\)
a: Sửa đề: \(\frac{3y}{28x^2}\cdot\frac{2x}{7y^4}\cdot49x^4y^3\)
\(=\frac{3y}{7y^4}\cdot\frac{2x}{28x^2}\cdot49x^4y^3\)
\(=\frac{3}{7y^3}\cdot\frac{1}{14x}\cdot49x^4y^3=\frac37\cdot\frac{1}{14}\cdot49\cdot\frac{x^4}{x}\cdot\frac{y^3}{y^3}=\frac37\cdot\frac72\cdot x^3=\frac32x^3\)
mình chỉ phân tích thôi
a) 6x(4-x)+x-4
=6x(4-x)-(4-x)
=(6x-1)(4-x)
c) 25x^2-10x+1-16z^2
=(5x-1)^2-16z^2
=(5x-1-4z)(5x-1+4z)
ban xem lại đề bài câu b đi chắc là sai đó
còn các câu trên bạn tự làm nhé
Thực hiện phép tính:
a) (2x-3y)(4x2+6xy+9y2)
=8x3-27y3
b) (6x3+3x2+4x+2):(3x2+2)
=(3x2+2)(2x+1):(3x2+2)
=2x+1
c) (x+2)2+(3-x)-2(x+3)(x-3)
=x2+4x+4+3-x-2x2+18
=-x2+4x+25
Bài 2:
a: 6x(4-x)+(x-4)
=6x(4-x)-(4-x)
=(4-x)(6x-1)
b: \(=x^2-1+y\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(1+y\right)=\left(y+1\right)\left(x+1\right)\left(x-1\right)\)
c: \(=\left(5x-1\right)^2-\left(4z\right)^2\)
=(5x-1-4z)(5x-1+4z)
a: \(=\dfrac{4x-2+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2x-1}{2x\left(2x-1\right)}\)
Bài 1:
a, (\(x\) - 4).(\(x\) + 4) - (5 - \(x\)).(\(x\) + 1)
= \(x^2\) - 16 - 5\(x\) - 5 + \(x^2\) + \(x\)
= (\(x^2\) + \(x^2\)) - (5\(x\) - \(x\)) - (16 + 5)
= 2\(x^2\) - 4\(x\) - 21
b, (3\(x^2\) - 2\(xy\) + 4) + (5\(xy\) - 6\(x^2\) - 7)
= 3\(x^2\) - 2\(xy\) + 4 + 5\(xy\) - 6\(x^2\) - 7
= (3\(x^2\) - 6\(x^2\)) + (5\(xy\) - 2\(xy\)) - (7 - 4)
= - 3\(x^2\) + 3\(xy\) - 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) \((2{x^2} - 7x + 4)( - 3{x^2} + 6x + 5)\)
\( = 2{x^2}( - 3{x^2} + 6x + 5) - 7x( - 3{x^2} + 6x + 5) + 4( - 3{x^2} + 6x + 5)\)
\( = 2{x^2}( - 3{x^2}) + 2{x^2}.6x + 2{x^2}.5 + 7x.3{x^2} - 7x.6x - 7x.5 + 4( - 3{x^2}) + 4.6x + 4.5\)
\(= - 6{x^4} + 33{x^3} - 44{x^2} - 11x + 20\)
a) \(x\left(x^2+4x+5\right)-x^2\left(x+4\right)\)
\(=x^3+4x^2+5x-x^3-4x^2\)
\(=5x\)
b) \(\left(x-2\right)^2+\left(3-x\right)\left(x-1\right)\)
\(=x^2-4x+4+3x-3-x^2+x\)
\(=1\)
c) \(\left(x+2\right)^3-x\left(x^2+6x+12\right)\)
\(=x^3+6x^2+12x+8-x^3-6x^2-12x\)
\(=8\)