Bài 1 . Tính GTNN
A= x^2 - 6x + 13
B= 2x^2 + 8x
C= 4x^2 +20x
Bài 2: Rút gọn biểu thức sau
a; (x + y )^3 - ( y -x )^3
b; (2x + 3y ) ( 2x - 3y ) - 40x ( x + 2) + 9y^2
Bài 3. Chứng minh
a, x^2 + 12x + 39 > 0
b, 4x^2 + 4x + 3 >0
BÀI 1 RÚT GỌN CÁC BIỂU THỨC SAU
a)(3x-2)(9x²+6x+4)-3(9x³-2)
b)(x²+4)(x+2)(x-2)-(x²+3)(x²-3)
c)(x+1)³-(x-1)(x²+x+1)-3x(x+1)
BÀI 2 CMR
a)-4x²-4x-2<0 với mọi x
Em ơi mình đăng bài sang bên môn toán nha
BÀI 1 RÚT GỌN CÁC BIỂU THỨC SAU
a)(3x-2)(9x²+6x+4)-3(9x³-2)
b)(x²+4)(x+2)(x-2)-(x²+3)(x²-3)
c)(x+1)³-(x-1)(x²+x+1)-3x(x+1)
BÀI 2 CMR
a)-4x²-4x-2<0 với mọi x
Bài 3. Rút gọn các đa thức sau
a/ (2x-3)(4x^2+6x+9)- (2x+1)(4x^2 - 2x +1)
b/ (x+ 2)(x^2- 2x+4) – (x^3- 2)
c/ (3x+ 5)(9x^2 - 15x +25)- 3x(3x-1)(3x+1)
d/ x^6 - (x^2 + x +1)(x^2 - 1)(x^2 - x+ 1)
a/ 2x\(^{^{ }3}\)-3\(^{^{ }3}\)-2x\(^3\)-1\(^{^{ }3}\)=-28
b/x\(^{^{ }3}\)+2\(^{^{ }3}\)-x\(^3\)+2=10
c/3x\(^3\)+5\(^3\)-3x(3x\(^2\)-1)=3x\(^3\)+5\(^3\)-3x\(^3\)+3x=125+3x
d/ x\(^6\)-(x\(^3\)+1)(x\(^2\)-x+1)= x\(^6\)-(x\(^6\)-x\(^4\)+x\(^3\)+x\(^2\)-x+1)=x\(^4\)-x\(^3\)-x\(^2\)+x-1
Rút gọn các biểu thức sau
a, \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
a: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
Bài 1: Thực hiện phép tính
a) (x-4) (x+4) - (5-x) (x+1)
b) (3x^2 - 2xy + 4) + ( 5xy - 6x^2 - 7)
Bài 2: Rút gọn biểu thức
a) 3x^2 (2x + y) - 2y(4x^2 - y)
b) (x+3y) (x-2y) - (x^4 - 6x^2y^3): x^2y
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
Bài 2:
a, 3\(x^2\).(2\(x\) + y) - 2y(4\(x^2\) - y)
= 6\(x^3\) + 3\(x^2\).y - 8y\(x^2\) + 2y2
= 6\(x^3\) - (8\(x^2\)y - 3\(x^2\)y) + 2y2
= 6\(x^3\) - 5\(x^2\)y + 2y2
Bài 1: Rút gọn các biểu thức sau:
a, A = (x-2).(2x-1) - 2x (x+3)
b, B = (3x-2).(2x+1) - (6x-1).(x+2)
c, C = 6x.(2x+3) - (4x-1).(3x-2)
d, D = (2x+3).(5x-2)+(x+4).(2x-1) - 6x.(2x-3)
Bài 2: Chứng tỏ rằng các đa thức không phụ thuộc vào biến.
a, 2x(3x-5).(x+11) - 3x.(2x+3).(x+7)
b, (x2+5x-6).(x-1) - (x+2).(x2-x+1) - x(3x-10)
c, (x2+x+1).(x-1) - x2(x+1) + x2 - 5
Bài 1
A= (x-2)(2x-1)-2x(x+3)=2x2-x-4x+2-2x2-6x=-11x+2
Bài 1:
a) \(A=\left(x-2\right)\left(2x-1\right)-2x\left(x+3\right)\)
\(A=2x^2-x-4x+2-2x^2-6x\)
\(A=-11x+2\)
b) \(B=\left(3x-2\right)\left(2x+1\right)-\left(6x-1\right)\left(x+2\right)\)
\(B=6x^2+3x-4x-2-6x^2-12x+x+2\)
\(B=-12x\)
c) \(C=6x\left(2x+3\right)-\left(4x-1\right)\left(3x-2\right)\)
\(C=12x^2+18x-12x^2+8x+3x-2\)
\(C=29x-2\)
d) \(D=\left(2x+3\right)\left(5x-2\right)+\left(x+4\right)\left(2x-1\right)-6x\left(2x-3\right)\)
\(D=10x^2-4x+15x-6+2x^2-x+8x-4-12x^2+18x\)
\(D=36x-10\)
Bài 2:
a: Ta có: \(2x\left(3x-5\right)\left(x+11\right)-3x\left(2x+3\right)\left(x+7\right)\)
\(=2x\left(3x^2+33x-5x-55\right)-3x\left(2x^2+14x+3x+21\right)\)
\(=6x^3+56x^2-110x-6x^2-51x^2-63x\)
\(=-117x\)
b: Ta có: \(\left(x^2+5x-6\right)\left(x-1\right)-\left(x+2\right)\left(x^2-x+1\right)-x\left(3x-10\right)\)
\(=x^3+4x^2-11x+6-\left(x^3-x^2+x+2x^2-2x+2\right)-3x^2+10x\)
\(=x^3+x^2-x+6-x^3-x^2+x-2\)
=4
c: Ta có: \(\left(x^2+x+1\right)\left(x-1\right)-x^2\left(x+1\right)+x^2-5\)
\(=x^3-1-x^3-x^2+x^2-5\)
=-6
rút gọn các biểu thức sau
a, \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
b, \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
a: \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\left(2x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1+2x-1\right)^2=\left(4x\right)^2=16x^2\)
b: \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
a) \(\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\left(2x+1\right)\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)
\(=\left(2x+1+2x-1\right)^2\)
\(=\left(4x\right)^2\)
\(=16x^2\)
b) \(\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=\left(x^3+2x^2-x-2\right)-\left(x^3-8\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
\(a,\left(2x+1\right)^2+2\left(4x^2-1\right)+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\cdot\left[\left(2x\right)^2-1^2\right]+\left(2x-1\right)^2\)
\(=\left(2x+1\right)^2+2\cdot\left(2x+1\right)\cdot\left(2x-1\right)+\left(2x-1\right)^2\)
\(=\left[\left(2x+1\right)+\left(2x-1\right)\right]^2\)
\(=\left(2x+1+2x-1\right)^2\)
\(=\left(4x\right)^2\)
\(=16x^2\)
\(---\)
\(b,\left(x^2-1\right)\left(x+2\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^2\left(x+2\right)-\left(x+2\right)-\left(x^3-2^3\right)\)
\(=x^3+2x^2-x-2-x^3+8\)
\(=2x^2-x+6\)
Rút gọn các biểu thức sau
a) (2x-1)2-3(x-1)(x+2)-(x-3)2
b) (x-2)(2x-1)-3(x+1)2-4x(x+2)
c) (x+2)(x2-3x+1)+(1-x)3
d) 3(x+2)(x-2)+(x-1)(2x+5)
a: \(\left(2x-1\right)^2-3\left(x-1\right)\left(x+2\right)-\left(x-3\right)^2\)
\(=4x^2-4x+1-x^2+6x-9-3\left(x^2+x-2\right)\)
\(=3x^2+2x-8-3x^2-3x+6\)
=-x+2
b: \(\left(x-2\right)\left(2x-1\right)-3\left(x+1\right)^2-4x\left(x+2\right)\)
\(=2x^2-x-4x+2-3x^2-6x-3-4x^2-8x\)
\(=-5x^2-19x-1\)
Bài 1. Tính:
32x^m. 1/2x
(a+5).4
(3a-5b).2a
(a^m+2a^3). a^n
x(2x+1)
-6x+3.(7+2x)
Bài 2. Tìm x: 3x+2(5-x)=0
Bài 3. Rút gọn biểu thức
6(3p+4q)-8(5p-q)+(p-q).
Bài 3. tính giá trị biểu thức sau khi rút gọn:
5x(4x^2-2x+1)- 2x(10x^2-5x-2) với x= -15.
Bài 2:
3x + 2(5 - x) = 0
<=> 3x + 10 - 2x = 0
<=> x + 10 = 0
<=> x = 0 - 10
<=> x = -10
=> x = -10
Bài 3:
6(3q + 4q) - 8(5p - q) + (p - q)
= 6.3p + 6.4q - 8.5p - (-8).q + p - q
= 18p + 24q - 40p + 8q + p - q
= (18p - 40p + p) + (24q + 8q - q)
= -21p + 31q
Bài 4:
5x(4x2 - 2x + 1) - 2x(10x2 - 5x - 2)
= 5x.4x2 + 5x.(-2x) + 5x.1 - 2x.10x2 + (-2x).(-5x) + (-2x).(-2)
= 20x3 - 10x2 + 5x - 20x3 + 10x2 + 4x
= (20x2 - 20x2) + (-10x2 + 10x2) + (5x + 4x)
= 0 + 0 + 9x
= 9x (1)
Thay x = -15 vào (1), ta có:
9.(-15) = -135
Vậy: Giá trị biểu thức sau khi rút gọn với x = -15 là: -135
Bài 2 rút gọn các biểu thức sau
A)(2x+3y)(x-2y)-(4x3y-6x2y2-3xy3):2xy
B) (x-2)3 -x(x+1)(x-1)-(3x-1)(3x-2)
a: \(\left(2x+3y\right)\left(x-2y\right)-\dfrac{\left(4x^3y-6x^2y^2-3xy^3\right)}{2xy}\)
\(=2x^2-4xy+3xy-6y^2-\dfrac{2xy\cdot\left(2x^2-3xy-1,5y^2\right)}{2xy}\)
\(=2x^2-xy-6y^2-2x^2+3xy+1,5y^2\)
\(=2xy-4,5y^2\)
b: \(\left(x-2\right)^3-x\left(x+1\right)\left(x-1\right)-\left(3x-1\right)\left(3x-2\right)\)
\(=x^3-6x^2+12x-8-x\left(x^2-1\right)-\left(9x^2-6x-3x+2\right)\)
\(=x^3-6x^2+12x-8-x^3+x-9x^2+9x-2\)
\(=-15x^2+22x-10\)