a) (2x + 3y)2
b) (x + \(\dfrac{1}{4}\))2
c) (x2 + \(\dfrac{2}{5}\)y) . (x2 - \(\dfrac{2}{5}\)y)
d) (2x + y2)3
e) (3x2 - 2y)2
f) (x + 4) (x2 - 4x + 16)
g) (x2 - \(\dfrac{1}{3}\)) . (x4 + \(\dfrac{1}{3}\)x2 + \(\dfrac{1}{9}\))
a) \(\left(2x+3y\right)^2=\left(2x\right)^2+2\cdot2x\cdot3y+\left(3y\right)^2=4x^2+12xy+9y^2\)
b) \(\left(x+\dfrac{1}{4}\right)^2=x^2+2\cdot x\cdot\dfrac{1}{4}+\left(\dfrac{1}{4}\right)^2=x^2+\dfrac{1}{2}x+\dfrac{1}{16}\)
c) \(\left(x^2+\dfrac{2}{5}y\right)\left(x^2-\dfrac{2}{5}y\right)=\left(x^2\right)^2-\left(\dfrac{2}{5}y\right)^2=x^4-\dfrac{4}{25}y^2\)
d) \(\left(2x+y^2\right)^3=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot y^2+3\cdot2x\cdot\left(y^2\right)^2+\left(y^2\right)^3=8x^3+12x^2y^2+6xy^4+y^6\)
e) \(\left(3x^2-2y\right)^2=\left(3x^2\right)^2-2\cdot3x^2\cdot2y+\left(2y\right)^2=9x^4-12x^2y+4y^2\)
f) \(\left(x+4\right)\left(x^2-4x+16\right)=x^3+4^3=x^3+64\)
g) \(\left(x^2-\dfrac{1}{3}\right)\cdot\left(x^4+\dfrac{1}{3}x^2+\dfrac{1}{9}\right)=\left(x^2\right)^3-\left(\dfrac{1}{3}\right)^3=x^6-\dfrac{1}{27}\)
Bài 5: Tìm nghiệm của các đa thức sau: Dạng 1: a) 4x + 9 b) -5x + 6 c) 7 – 2x d) 2x + 5 Dạng 2: a) ( x+ 5 ) ( x – 3) b) ( 2x – 6) ( x – 3) c) ( x – 2) ( 4x + 10 ) Dạng 3: a) x2 -2x b) x2 – 3x c) 3x2 – 4x d) ( 2x- 1)2 Dạng 4: a) x2 – 1 b) x2 – 9 c)– x 2 + 25 d) x2 - 2 e) 4x2 + 5 f) –x 2 – 16 g) - 4x4 – 25 Dạng 5: a) 2x2 – 5x + 3 b) 4x2 + 6x – 1 c) 2x2 + x – 1 d) 3x2 + 2x – 1
Phân tích
a,(x2 + x + 2)3 - (x+1)3 = x6 +1 b,(x2 + 10x + 8)2 - (8x + 4)(x2 + 8x+7)
c, A= x4 + 2x3 + 3x2 + 2x+4 d,B= x4 + 4x3 + +8x2 + 8x + 4
e, C= x4 - 2x3 + 5x2 - 4x + 4
1) Rut gon cac bieu thuc sau :
a) (x-3)(x2+3x+ 9)-(54+x3)
b) (3x+y)(9x2-3xy +y2)-(3x-y)(9x2+3xy+y2)
2, Dien cac don thuc thich hop vao cho trong
a, (x+3y) (... - ... + ...) = x^3 +27y^3
b, (2x- ....) (... + 6xy + ... +...) = 8x^3 - 27y^3
\(1.\)
\(a.\)
\(\left(x-3\right)\left(x^2+3x+9\right)-\left(54+x^3\right)\)
\(=\left(x^3-3^3\right)-\left(54+x^3\right)\)
\(=x^3-27-54-x^3\)
\(=-81\)
\(b.\)
\(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
\(=\left(27x^3+y^3\right)-\left(27x^3-y^3\right)\)
\(=27x^3+y^3-27x^3+y^3\)
\(=2y^3\)
\(2.\)
\(a.\)
\(\left(x+3y\right)\left(x^2-3xy+9y^2\right)=x^3+27y^3\)
\(b.\)
\(\left(2x-3y\right)\left(4x^2+6xy+9y^3\right)=8x^3-27y^3\)
1) a) \(\left(x-3\right)\left(x^2+3x+9\right)-\left(54+x^3\right)\)
\(=\left(x^3-3^3\right)-\left(54+x^3\right)\\ =\left(x^3-27\right)-54-x^3\\ =-27-54\\ =-81\)
b) \(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
\(=\left[\left(3x\right)^3+y^3\right]-\left[\left(3x\right)^3-y^3\right]\\ =2y^3\)
2) a) \(\left(x+3y\right)\left(x^2-3xy+9y^2\right)=x^3+27y^3\)
b) \(\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)=8x^3-27y^3\)
1.(x2+3).(x4-3x2+9)
2.(2x+1).(4x2-2x+1)
3.(x2+2).(x4-2x2+4)
4.(3x+2).(9x2-6x+4)
\(1,=x^6+27\\ 2,=8x^3+1\\ 3,=x^6+8\\ 4,=27x^3+8\)
1. (x2 + 3)(x4 - 3x2 + 9)
= x6 + 27
2. (2x + 1)(4x2 - 2x + 1)
= 8x3 + 1
3. (x2 + 2)(x4 - 2x2 + 4)
= x6 + 8
4. (3x + 2)(9x2 - 6x + 4)
= 27x3 + 8
1: \(\left(x^2+3\right)\left(x^4-3x^2+9\right)=x^6+27\)
2: \(\left(2x+1\right)\left(4x^2-2x+1\right)=8x^3+1\)
3: \(\left(x^2+2\right)\left(x^4-2x^2+4\right)=x^6+8\)
4: \(\left(3x+2\right)\left(9x^2-6x+4\right)=27x^3+8\)
bai 1. 11/3.40/13+37/5:7/33-(11/13.1/3+33/7:5/2)
bai 2.tim x
a,3.(x-1)-5.(-7)=(-2)^3-2x
b,2./(1-x)^2+1/-2^2.3=8
bai 3,cho bieu thuc
M=n+1/n+1 - 3-8n/n+1 + 8/n+1
tim cac gia tri cua n de bieu thuc M co gia tri la so nguyen
bai 4,So hoc sinh cua 1 truong ko qua 1000 em,neuxeptoan bo so hoc sinh cua truong do thanh cac hang,moi hang 20 nguoi thi con thieu 5 nguoi,neu xep moi hang 25 nguoi hoac 30 nguoi thi deu thua 15 nguoi , neu xep 42 hang thi vua du . hoi truong do co bao nhieu hoc sinh
bai 5,cho bieu thuc
A=2+2^2+...+2^200
c/m rang
a, A+2 la 1 luy thua cua 2
b, Achia het cho 30
c,A co phai la so chinh phuong ko ? vi sao ?
bai 6,cho 2 bieu thuc
A=1/1+2 + 1/1+2+3 + ...1/1+2+3+...+99
B=1 + 1/2^2+1/3^2 + ...+1/49^2
c/m rang A<B
3(x-1)-5x(-7)=-2^3-2x
3x-3x1--35=-8-2x
3x+32=-8-2x
3x+2x=-8-32
5x=-40
x=-40:5
x=-8
Rút gọn
a) (x2−1)3−(x4+x2+1)(x2−1)(x2−1)3−(x4+x2+1)(x2−1)
b) (x4−3x2+9)(−x2+3)−(3+x2)3(x4−3x2+9)(−x2+3)−(3+x2)3
c) (x+y)3−(x−y)3−6x2y
Giải hộ e bài này với ai 👍
Câu 1 : a, 4x2 -3x-1=0 / d, 4x4-5x2+1=0
b, x2 - (1+căn 5)x + căn 5= 0 / e,x2 +3=|4x| / f, 2x + 5cănx +3 =0 / g, (x2 +x +1 ).(x2+x+2)=2 / h, x4-5x2+4=0
c, x4 + x2 -20=0 / k, x phần x2-1 -- 1 phần 2(x+1) = 1phan 2
a) 2x2(x-2)+3x(x2-x-2)-5(3-x2)
b) (x-1)(x-3)-(4-x)(2x+1)-3x2+2x-5
c) (x4-x3-3x2+x+2):(x2-1)
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