K
Khách

Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.

20 tháng 6 2019

phân tích đa thức thành nhân tử đi

20 tháng 6 2019

1a) A = \(x^2-4x+2023=\left(x-2\right)^2+2019\)

Ta luôn có: (x - 2)2 \(\ge\)\(\forall\)x

 => (x - 2)2 + 2019 \(\ge\)2019 \(\forall\)x

Hay A \(\ge\)\(\forall\)x

Dấu "=" xảy ra khi : (x - 2)2 = 0 => x - 2 = 0 => x = 2

Nên Amin = 2019 khi x = 2

22 tháng 7 2019

\(A=x^2+3x+7\)

\(=x^2+2.1,5x+2,25+4,75\)

\(=\left(x+1,5\right)^2+4,75\ge4,75\)

Vậy \(A_{min}=4,75\Leftrightarrow x=-1,5\)

22 tháng 7 2019

\(B=2x^2-8x\)

\(=2\left(x^2-4x\right)\)

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

\(=2\left[\left(x-2\right)^2-4\right]\)

\(=2\left(x-2\right)^2-8\ge-8\)

Vậy \(B_{min}=-8\Leftrightarrow x=2\)

1. tính a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\) b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\) c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\) d) \(\left(\dfrac{1}{2}x-2y\right)^3\) e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\) f) \(27x^3-8y^3\) g) 4(2x - 3y) - 4 - (2x-3y)2 2. rút gọn a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\) b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\) c)...
Đọc tiếp

1. tính

a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)

b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)

c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)

d) \(\left(\dfrac{1}{2}x-2y\right)^3\)

e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)

f) \(27x^3-8y^3\)

g) 4(2x - 3y) - 4 - (2x-3y)2

2. rút gọn

a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)

b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)

c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)

d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)

3. c/m các biểu thức sau ko phụ thuộc vào biến x,y

a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)

b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)

c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)

d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)

4. Tìm x

a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)

b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)

c) \(49x^2+14x+1=0\)

d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)

5. c/m biểu thức luôn dương:

a) \(A=16x^2+8x+3\)

b) \(B=y^2-5y+8\)

c) C= \(2x^2-2x+2\)

d) \(D=9x^2-6x+25y^2+10y+4\)

6. Tìm GTLN và GTNN của các biểu thức sau

a) \(M=x^2+6x-1\)

b) \(N=10y-5y^2-3\)

7. thu gọn

a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)

b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)

2
9 tháng 9 2017

Bạn đăng từ từ thôi!

Dài quá

18 tháng 2 2020

Bài 2 :

a) \(\left(5x^2y-8xy^2+y^3\right)\left(2x^3+x^2y-3y^2\right)\)

\(=10x^5y+5x^4y^2-15x^2y^3-16x^4y^2-8x^3y^3+24xy^4+2x^3y^3+x^2y^4-3y^5\)

\(=10x^5y-11x^4y^2-6x^3y^3+x^2y^4-15x^2y^3+24xy^4-3y^5\)

6 tháng 3 2018

Hỏi đáp Toán

Bài 1: Phân tích đa thức thành nhân tử: a) \(2x\left(x+1\right)+2\left(x+1\right)\) b) \(y^2\left(x^2+y\right)-zx^2-zy\) c) \(4x\left(x-2y\right)+8y\left(2y-x\right)\) d) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\) e) \(x^2-6xy+9y^2\) f) \(x^3+6x^2y+12xy^2+8y^3\) g) \(x^3-64\) h) \(125x^3+y^6\) k) \(0,125\left(a+1\right)^3-1\) t) \(x^2-2xy+y^2-xz+yz\) q) \(x^2-y^2-x+y\) p) \(a^3x-ab+b-x\) đ)...
Đọc tiếp

Bài 1: Phân tích đa thức thành nhân tử:

a) \(2x\left(x+1\right)+2\left(x+1\right)\)

b) \(y^2\left(x^2+y\right)-zx^2-zy\)

c) \(4x\left(x-2y\right)+8y\left(2y-x\right)\)

d) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)

e) \(x^2-6xy+9y^2\)

f) \(x^3+6x^2y+12xy^2+8y^3\)

g) \(x^3-64\)

h) \(125x^3+y^6\)

k) \(0,125\left(a+1\right)^3-1\)

t) \(x^2-2xy+y^2-xz+yz\)

q) \(x^2-y^2-x+y\)

p) \(a^3x-ab+b-x\)

đ) \(3x^2\left(a+b+c\right)+36xy\left(a+b+c\right)+108y^2\left(a+b+c\right)\)

l) \(x^2-x-6\)

i) \(x^4+4x^2-5\)

m) \(x^3-19x-30\)

j) \(x^4+x+1\)

y) \(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)

o) \(\left(a+b+c\right)^3-a^3-b^3-c^3\)

ê) \(4a^2b^2-\left(a^2+b^2+c^2\right)^2\)

w) \(\left(1+x^2\right)^2-4x\left(1-x^2\right)\)

z) \(\left(x^2-8\right)^2+36\)

u) \(81x^4+4\)

Bài 2 : Tìm x

a)\(\left(2x-1\right)^2-25=0\)

b) \(8x^3-50x=0\)

c) \(\left(x-2\right)\left(x^2+2+7\right)+2\left(x^2-4\right)-5\left(x-2\right)=0\)

d) \(3x\left(x-1\right)+x-1=0\)

e) \(2\left(x+3\right)-x^2-3x\) =0

f) \(4x^2-25-\left(2x-5\right)\left(2x+7\right)=0\)

g) \(x^3+27+\left(x+3\right)\left(x-9\right)=0\)

5
12 tháng 10 2017

Bài 1 :

a ) \(2x\left(x+1\right)+2\left(x+1\right)=\left(x+1\right)\left(2x+2\right)=2\left(x+1\right)^2\)

b ) \(y^2\left(x^2+y\right)-zx^2-zy=y^2\left(x^2+y\right)-z\left(x^2+y\right)=\left(x^2+y\right)\left(y^2-z\right)\)

c ) \(4x\left(x-2y\right)+8y\left(2y-x\right)=4x\left(x-2y\right)-8y\left(x-2y\right)=4\left(x-2y\right)^2\)

d ) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)=\left(x+1\right)\left(3x-2x^2+7\right)\)

e ) \(x^2-6xy+9y^2=\left(x-3x\right)^2\)

12 tháng 10 2017

Bài 1 :

f ) \(x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\)

g ) \(x^3-64=\left(x-4\right)\left(x^2+4x+16\right)\)

h ) \(125x^3+y^6=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)

17 tháng 11 2022

a: \(=4x^2-25-4x^2+12x-9-12x=-34\)

b: \(=8y^3-12y^2+6y-1-2y\left(4y^2-12y+9\right)-12y^2+12y\)

\(=8y^3-24y^2+18y-1-8y^3+24y^2-18y=-1\)

c: \(=x^3+27-x^3-20=7\)

d: \(=3y\left(9y^2+12y+4\right)-27y^3+1-36y^2-12y-1\)

\(=27y^3+36y^2+12y-27y^3-36y^2-12y\)

=0

14 tháng 8 2018

B = (x-1)(2x+1) - (x2-2x-1)

B = 2x2+x-2x-1-x2-2x-1 = x2-3x-2

B = x2+x-4x-2 = x(x+1) - 4(x+1)

B = (x+1)(x-4)

14 tháng 8 2018

\(A=2x\left(x-2\right)-x\left(2x-3\right)\\ =2x^2-4x-2x^2+3x\\ =-x\\ B=\left(x-1\right)\left(2x+1\right)-\left(x^2-2x-1\right)\\ =x\left(2x+1\right)-\left(2x+1\right)-x^2+2x+1\\ =2x^2+x-2x-1-x^2+2x+1\\ =x^2+x\\ C=\left(x+y\right)\left(x^2-xy+y^2\right)-x^3\\ =x\left(x^2-xy+y^2\right)+y\left(x^2-xy+y^2\right)-x^3\\ =x^3-x^2y+xy^2+x^2y-xy^2+y^3-x^3\\ =y^3\)

\(D=\left(12x-3\right)\left(x+4\right)-x\left(2x+7\right)\\ =x\left(12x-3\right)+4\left(12x-3\right)-2x^2-7x\\ =12x^2-3x+48x-12-2x^2-7x\\ =10x^2+38x-12\\ E=\left(2x+y\right)\left(4x^2-2xy+y^2\right)\\ =2x\left(4x^2-2xy+y^2\right)+y\left(4x^2-2xy+y^2\right)\\ =8x^3-4x^2y+2xy^2+4x^2y-2xy^2+y^3\\ =8x^3+y^3\)

11 tháng 7 2019

\(a,3x^3y^3-15x^2y^2=3x^2y^2\left(xy-5\right)\)

\(b,5x^3y^2-25x^2y^3+40xy^4\)

\(=5xy^2\left(x^2-5xy+8y^2\right)\)

\(c,-4x^3y^2+6x^2y^2-8x^4y^3\)

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

\(d,a^3x^2y-\frac{5}{2}a^3x^4+\frac{2}{3}a^4x^2y\)

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

\(e,a\left(x+1\right)-b\left(x+1\right)=\left(x+1\right)\left(a-b\right)\)

\(f,2x\left(x-5y\right)+8y\left(5y-x\right)\)

\(=2x\left(x-5y\right)-8y\left(x-5y\right)=\left(x-5y\right)\left(2x-8y\right)\)

\(g,a\left(x^2+1\right)+b\left(-1-x^2\right)-c\left(x^2+1\right)\)

\(=\left(x^2+1\right)\left(a-b-c\right)\)

\(h,9\left(x-y\right)^2-27\left(y-x\right)^3\)

\(=9\left(x-y\right)^2+27\left(x-y\right)^3\)

\(=9\left(x-y\right)^2\left(1+3x-3y\right)\)

11 tháng 7 2019

a,3x3y315x2y2=3x2y2(xy5)a,3x3y3−15x2y2=3x2y2(xy−5)

b,5x3y225x2y3+40xy4b,5x3y2−25x2y3+40xy4

=5xy2(x25xy+8y2)=5xy2(x2−5xy+8y2)

c,4x3y2+6x2y28x4y3c,−4x3y2+6x2y2−8x4y3

=2x2y2(2x3+4x2y)=−2x2y2(2x−3+4x2y)

d,a3x2y52a3x4+23a4x2yd,a3x2y−52a3x4+23a4x2y

=a3x2(y52x2+23ay)=a3x2(y−52x2+23ay)

e,a(x+1)b(x+1)=(x+1)(ab)e,a(x+1)−b(x+1)=(x+1)(a−b)

f,2x(x5y)+8y(5yx)f,2x(x−5y)+8y(5y−x)

=2x(x5y)8y(x5y)=(x5y)(2x8y)=2x(x−5y)−8y(x−5y)=(x−5y)(2x−8y)

g,a(x2+1)+b(1x2)c(x2+1)g,a(x2+1)+b(−1−x2)−c(x2+1)

=(x2+1)(abc)=(x2+1)(a−b−c)

h,9(xy)227(yx)3h,9(x−y)2−27(y−x)3

=9(xy)2+27(xy)3