Rút gọn
4x(x2 - 2x + 3) - 3x (x + 1)(x - 2) + ( 2x - 5)(x-7)-4x(x2-x+1)
Bài 1 Rút gọn biểu thức
a, [(3x - 2)(x + 1) - (2x + 5)(x2 - 1)] : (x + 1)
b, (2x + 1)2 - 2(2x + 1)(3 - x) + (3 - x)2
c, (x - 1)2 - (x + 1) (x2 - x + 1) - (3x + 1)(1 - 3x)
d, (x2 + 1)(x - 3) - (x - 3)(x2 + 3x + 9)
e, (3x +2)2 + (3x - 2)2 - 2(3x + 2)(3x - 2) + x
Bài 2 Phân tích các đa thức sau thành nhân tử
1, 3(x + 4) - x2 - 4x
2, x2 - xy + x - y
3, 4x2 -25 + (2x + 7)(5 - 2x)
4, x2 + 4x - y2 + 4
5, x3 - x2 - x + 1
6, x3 + x2y - 4x - 4y
7, x3 - 3x2 + 1 - 3x
8, 2x2 + 3x - 5
9, x2 - 7xy + 10y2
10, x3 - 2x2 + x - xy2
rút gọn A,B,C
A=(3x+7)(2x+3)-(3x-5)(2x+11)
B=(x2-2)(x2+x-1)-x(x3+x2-3x-2)
C=x(x3+x2-3x-2)-(x2-2)(x2+x-1)
\(A=6x^2+23x+21-\left(6x^2+23x-55\right)=76\\ B=x^4+x^3-x^2-2x^2-2x+2-x^4-x^3+3x^2+2x\\ =2\\ C=x^4+x^3-3x^2-2x-\left(x^4+x^3-x^2-2x^2-2x+2\right)\\ =-2\)
Bài 1: Rút gọn
C) (x2 - 3) (x2 +3) - 5x2 (x + 1)2 - (x2 - 3x) ( x2 - 2x) + 4x (x + 2)2
D) -6x2 (x + 5)2 - ( x - 3)2 + (x2 - 2) (2x2 + 1) - 4x2 ( 3x - 4)2
A) -2x(3x+2)(3x-2)+5(x+2)2 - (x-1)(2x+1)(2x+1)
= -2x(9x2-4)+5(x2+4x+4) - (x-1)(4x2-1)
= -18x3+8x+5x2+20x+20-(4x3-x-4x2+1)
= -18x3+5x2+28x+20-4x3+x+4x2+1
= -22x3+9x2+29x+21
B) (7x-8)(7x+8)-10(2x+3)2+5x(3x-2)2-4x(x-5)2
= 49x2 - 64 -10(4x2+ 12x + 3) + 5x(9x2 - 12x +4) - 4x(x2 - 10x +25)
= 49x2 - 64 -40x2 - 120x - 30 + 45x3 - 60x2 - 20x - 4x3 + 40x2 -100x
= 41x3 -11x2 -240x -94
C) \(\left(x^2-3\right)\left(x^2+3\right)-5x^2\left(x+1\right)^2-\left(x^2-3x\right)\left(x^2-2x\right)+4x\left(x+2\right)^2\)
\(\left(x^4-9\right)-5x^2\left(x^2+2x+1\right)-\left(x^4-2x^3-3x^3+6x^2\right)+4x\left(x^2+4x+4\right)\)
\(x^4-9-5x^4-10x^3-5x^2-x^4+5x^3-6x^2+4x^3+16x^2+16x\)
\(-5x^4-x^3+5x^2+20x-9\)
D) \(-6x^2\left(x+5\right)^2-\left(x-3\right)^2+\left(x^2-2\right)\left(2x^2+1\right)-4x^2\left(3x-4\right)^2\)
\(-6x^2\left(x^2+10x+25\right)-\left(x^2-6x+9\right)+2x^4-3x^2-2-4x^2\left(9x^2-24x+16\right)\)
\(-6x^4-60x^3+150x^2-x^2+6x-9+2x^4-3x^2-2-36x^4+96x^3-64x^2\)
\(-40x^4+36x^3+82x^2+6x-11\)
1) Rút gọn C = ( 3x- 5) ( 2x + 11 ) - (2x + 3) ( 3x + 7)
2) Thực hiện phép tính ( 2x4+ 2x3 - 7x2 -x +3) : ( 2x2 - 1)
3) Tìm x : ( x+ 4) ( x2 - 4x + 16) - x ( x- 5) (x+ 5) = 264
Bài 3:
\(\Leftrightarrow x^3+64-x^3+25x=264\)
hay x=8
\(1,C=6x^2+23x-55-6x^2-23x-21=-76\\ 2,=\left(2x^4-x^2+2x^3-x-6x^2+6-3\right):\left(2x^2-1\right)\\ =\left[\left(2x^2-1\right)\left(x^2+x-6\right)-3\right]:\left(2x^2-1\right)\\ =x^2+x-6\left(dư.-3\right)\\ 3,\Leftrightarrow x^3+64-x^3+25x=264\\ \Leftrightarrow25x=200\Leftrightarrow x=8\)
tìm x:
a)3(2x-3)+2(2-x)=-3
b)2x(x2-2)+x2(1-2x)-x2=-12
c)3x(2x+3)-(2x+5)(3x-2)=8
d)4x(x - 1) - 3(x2-5)-x2=(x-3)-(x+4)
e)2(3x-1)(2x+5)-6(2x-1)(x+2)=-6
a: Ta có: \(3\left(2x-3\right)+2\left(2-x\right)=-3\)
\(\Leftrightarrow6x-9+4-2x=-3\)
\(\Leftrightarrow4x=2\)
hay \(x=\dfrac{1}{2}\)
Bài 3: Rút gọn các biểu thức sau:
1) ( x+ 3)(x2 -3x + 9) - (x3 + 54)
2) (2x + y)(4x2 + 2xy + y2 ) - (2x – y)(4x2 + 2xy + y2 )
3) (x – 1)3 – (x + 2)(x2 -2x +4) +3(x +4)(x – 4)
4) x(x + 1)(x - 1) – (x + 1)(x2 – x +1)
5) 8x3 - 5 (2x + 1)(4x2 – 4x + 1)
6) 27 + (x – 3)(x2 +3x + 9)
7) (x – 1)3 – (x +2)(x2 -2x + 4) +3(x +4)(x -4)
8) (x – 2)3 +6( x – 1)2 –(x +1)(x2 -x +1) +3x
1: Ta có: \(\left(x+3\right)\left(x^2-3x+9\right)-\left(x^3+54\right)\)
\(=x^3+27-x^3-54\)
=-27
2: Ta có: \(\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3\)
\(=2y^3\)
\(1,=x^3+270-x^3-54=-27\\ 2,=8x^3+y^3-8x^3+y^3=2y^3\\ 3,=x^3-3x^2+3x-1-x^3-8+3x^2-48=3x-57\\ 4,=x^3-x-x^3-1=-x-1\\ 5,=8x^3-5\left(8x^3+1\right)=-32x^3-5\\ 6,=27+x^3-27=x^3\\ 7,làm.ở.câu.3\\ 8,=x^3-6x^2+12x-8+6x^2-12x+6-x^3-1+3x\\ =3x-3\)
1) (3x - 2)(4x + 5) = 0
2) (4x + 2)(x2 + 3) = 0
3) (2x + 7)(x - 3)(5x - 1) = 0
4) x2 - 3x = 0
5) x2 - x = 0
1
(3x-2)(4x+5)=0
⇔ 3x-2=0 -> x= 2/3
⇔ 4x-5=0 x= 5/4
Vậy tập nghiệm S = { 2/3; 5/4}
2, (4x+2)(\(X^2\)+3)=0
⇔ 4x+2=0 -> x= -1/2
\(x^2\)+3=0 -> x= \(\sqrt{3}\); -\(\sqrt{3}\)
Vaayj tập nghiệm S= { -1/2; \(\sqrt{3}\);-\(\sqrt{3}\)}
3)
(2x+7)(x-3)(5x-1)=0
⇔ 2x+7=0 -> x= -7/2
x-3 =0 -> x = 3
5x-1 =0 -> x= 1/5
Vậy tập nghiệm S={ -7/2; 3; 1/5}
a)9x2 – 49 = 0
b)(x – 1)(x + 2) – x – 2 = 0
c)(4x + 1)(x - 2) - (2x -3)(2x + 1) = 7
d)x(3x + 2) + (x + 1)2 – (2x – 5)(2x + 5) = 0
e)(x + 3)(x2 – 3x + 9) –x(x – 1)(x + 1) – 27 = 0
f)(4x-3)^2-3x(3-4x)=0
\(a,\Leftrightarrow\left(3x-7\right)\left(3x+7\right)=0\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{3}\\x=-\dfrac{7}{3}\end{matrix}\right.\\ b,\Leftrightarrow\left(x+2\right)\left(x-1-1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\\ c,\Leftrightarrow4x^2-7x-2-4x^2+4x+3=7\\ \Leftrightarrow-3x=6\Leftrightarrow x=-2\\ d,\Leftrightarrow3x^2+2x+x^2+2x+1-4x^2+25=0\\ \Leftrightarrow4x=-26\Leftrightarrow x=-\dfrac{13}{2}\\ e,\Leftrightarrow x^3+27-x^3+x-27=0\\ \Leftrightarrow x=0\\ f,\Leftrightarrow\left(4x-3\right)\left(4x-3+3x\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{4}\\x=\dfrac{3}{7}\end{matrix}\right.\)
a) 9x2-49=0
(3x)2-72=0
<=> (3x-7)(3x+7)=0
th1: 3x-7=0
<=>3x=7
<=>x=\(\dfrac{7}{3}\)
th2: 3x+7=0
<=>3x=-7
<=>x=\(-\dfrac{7}{3}\)
Bài 1: Thu gọn các biểu thức sau
a)(2x2 + 5x - 2)(2x2 - 4x +3)
b)(2x -3)(3x - 2) - 3x(2x - 5)
c)(x -1)(x2 + x + 1) - (x + 1)(x2 - x +1)
d)(x2 + x - 1)(x2 - x + 1)
e)(2 + 3y)2 - (2x -3y)2 -12xy
d)(x2 - 4x)(5 + 2x - x2)
cảm ơn!giúp mình với chiều nay ktra 15ph T_T
Bài 2. Rút gọn các biểu thức sau :
A = (x - 3)(x + 7) – (x + 5)(x - 1) B = - 2(2x + 5)2 – (4x + 1)(1 – 4x)
C = x2(x – 4)(x + 4) – (x2 + 1)(x2 - 1) D = (x + 1)(x2 – x + 1) – (x – 1)(x2 + x +1)
E = (x – 1)3 – (x – 1)(x2 + x + 1) – (3x + 1)(1 – 3x)
\(A=x^2+4x-21-x^2-4x+5=-16\\ B=-2\left(4x^2+20x+25\right)-\left(1-16x^2\right)\\ B=-8x^2-40x-50-1+16x^2=8x^2-40x-51\\ C=x^2\left(x^2-16\right)-\left(x^4-1\right)=x^4-16x^2-x^4+1=1-16x^2\\ D=x^3+1-\left(x^3-1\right)=2\\ E=x^3-3x^2+3x-1-x^3+1-9x^2+1=-12x^2+3x+1\)