II.Rút gọn biểu thức
A=(x-2)2+(x+3)2-2(x+1)(x-1)
B=(x-y)(x+y)(x2+y2)(x4+y4)(x8+y8)
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NM
3
AD
15 tháng 10 2023
\(x\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\left(x-y\right)+xy^{16}\\ =x\left(x+y\right)\left(x-y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\\ =x\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\\ =x\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\\ =x\left(x^8-y^8\right)\left(x^8+y^8\right)+xy^{16}\\ =x\left(x^{16}-y^{16}\right)+xy^{16}\\ =x^{17}-xy^{16}+xy^{16}\\ =x^{17}\)
H9
HT.Phong (9A5)
CTVHS
15 tháng 10 2023
\(x\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\left(x-y\right)+xy^{16}\)
\(=x\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)
\(=x\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)
\(=x\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)+xy^{16}\)
\(=x\left(x^8-y^8\right)\left(x^8+y^8\right)+xy^{16}\)
\(=x\left(x^{16}-y^{16}\right)+xy^{16}\)
\(=x^{17}-xy^{16}+xy^{16}\)
\(=x^{17}\)
18 tháng 10 2021
a) \(=6a-3+15-5a=a+12\)
b) \(=25x-12x+4+35-14x=-x+39\)
d) \(=2ab+8a^2-b^2-4ab+2ab-6a^2=2a^2-b^2\)
e) \(=x+x^2-x^3+x^4-x^5+1+x-x^2+x^3-x^4=-x^5+2x+1\)
f) \(=6y^3-3y^2+y-y+y^2-y^3-y^2+y=5y^3-3y^2+y\)
PL
18 tháng 10 2021
a) 3( 2a -1) +5( 3-a)
= 3. 2a -3.1 +5. 3- 5.a
= 6a -3+ 15-5a
=(6a -5a )+ (-3+ 15)
b) 25x - 4(3x - 1) +7(5 - 2x)
= 25x -4.3x + 4.1 + 7.5 - 7.2
=25x - 12x + 4 +35 - 14x
= (25x-12x-14x)+(4+35)
= -x=39
c) -12x3 -x1-2x-18x2
= -36x-x-2x-36x
= -75x
d) (2a-b)(b+4a)+2a(b-3a)
= 2ab+2a4a-bb-b4a+2ab-2a3b
= 2ab+8a2-b2-4ab+2ab-6a2
=(2ab-4ab+2ab)+(8a2-6a2)-b2
= 2a2-b2
e) (x+1)(2+x-x2+x3-x4)
= (x+1)(2-2x)
= x2-x2x+1.2-1.2x
=(2x-2x)-2x2+2
= -2x2+2
15 tháng 7 2021
B1
a, \(=>A=\left(x+y+x-y\right)\left(x+y-x+y\right)=2x.2y=4xy\)
b, \(=>B=\left[\left(x+y\right)-\left(x-y\right)\right]^2=\left[x+y-x+y\right]^2=\left[2y\right]^2=4y^2\)
c,\(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)
\(=\)\(\left(x+1\right)\left(x^2-x+1\right)\left(x-1\right)\left(x^2+x+1\right)=\left(x^3+1^3\right)\left(x^3-1^3\right)=x^6-1\)
d, \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a-b+c\right)^2-\left(b-c\right)^2\)
\(=\left(a+b-c+b-c\right)\left(a+b-c-b+c\right)\)
\(+\left(a-b+c+b-c\right)\left(a-b+c-b+c\right)\)
\(=a\left(a+2b-2c\right)+a\left(a-2b\right)\)
\(=a\left(a+2b-2c+a-2b\right)=a\left(2a-2c\right)=2a^2-2ac\)
B2:
\(\)\(x+y=3=>\left(x+y\right)^2=9=>x^2+2xy+y^2=9\)
\(=>xy=\dfrac{9-\left(x^2+y^2\right)}{2}=\dfrac{9-\left(17\right)}{2}=-4\)
\(=>x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)=3\left(17+4\right)=63\)
15 tháng 7 2021
Bài 1:
a) Ta có: \(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=x^2+2xy+y^2-x^2+2xy+y^2\)
=4xy
b) Ta có: \(\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x+y-x+y\right)^2\)
\(=\left(2y\right)^2=4y^2\)
c) Ta có: \(\left(x^2+x+1\right)\left(x^2-x+1\right)\left(x^2-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)\left(x+1\right)\left(x^2-x+1\right)\)
\(=\left(x^3-1\right)\left(x^3+1\right)\)
\(=x^6-1\)
d) Ta có: \(\left(a+b-c\right)^2+\left(a+b+c\right)^2-2\left(b-c\right)^2\)
\(=\left(a+b-c\right)^2-\left(b-c\right)^2+\left(a+b+c\right)^2-\left(b-c\right)^2\)
\(=\left(a+b-c-b+c\right)\left(a+b-c+b-c\right)+\left(a+b+c-b+c\right)\left(a+b+c+b-c\right)\)
\(=a\cdot\left(a+2b-2c\right)+\left(a+2c\right)\left(a-2b\right)\)
\(=a^2+2ab-2ac+a^2-2ab+2ac-4bc\)
\(=2a^2-4bc\)
19 tháng 8 2021
a: Ta có: \(y\left(x^2-y^2\right)\cdot\left(x^2+y^2\right)-y\left(x^4-y^4\right)\)
\(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)\)
=0
b: Ta có: \(\left(2x+\dfrac{1}{3}\right)\left(4x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)-\left(8x^3-\dfrac{1}{27}\right)\)
\(=8x^3+\dfrac{1}{27}-8x^3+\dfrac{1}{27}\)
\(=\dfrac{2}{27}\)
c: Ta có: \(\left(x-1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(1-x\right)\)
\(=x^3-3x^2+3x-1-x^3+1-3x+3x^2\)
=0
17 tháng 10 2021
\(a,=x^3-16x-x^2-1-x^2+1=x^3-2x^2-16x\\ b,=y^4-81-y^4+4=-77\\ d,=a^2+b^2+c^2+2ab-2bc-2ac+a^2-2ac+c^2-2ab-2ac\\ =2a^2+b^2+2c^2-2bc-6ac\)
21 tháng 10 2021
a: \(\left(2x-1\right)^2-2\left(2x-3\right)^2+4\)
\(=4x^2-4x+1+4-2\left(4x^2-12x+9\right)\)
\(=4x^2-4x+5-8x^2+24x-18\)
\(=-4x^2+20x-13\)
e: \(\left(2x+3y\right)\left(4x^2-6xy+9y^2\right)=8x^3+27y^3\)
25 tháng 8 2021
a) \(A=y\left(x^2-y^2\right)\left(x^2+y^2\right)-y\left(x^4-y^4\right)=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)=0\)
b) \(B=\left(x-1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3\left(1-x\right)x=x^3-3x^2+3x-1-x^3-x^2-x+x^2+x+1-3x+3x^2=0\)
25 tháng 8 2021
a: Ta có: \(A=y\left(x^2-y^2\right)\left(x^2+y^2\right)-y\left(x^4-y^4\right)\)
\(=y\left(x^4-y^4\right)-y\left(x^4-y^4\right)\)
=0
b: Ta có: \(B=\left(x-1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(1-x\right)\)
\(=x^3-3x^2+3x-1-x^3+1-3x+3x^2\)
=0
KV
3 tháng 8 2023
(x - 5)² = (3 + 2x)²
(x - 5)² - (3 + 2x)² = 0
[(x - 5) - (3 + 2x)][(x - 5) + (3 + 2x)] = 0
(x - 5 - 3 - 2x)(x - 5 + 3 + 2x) = 0
(-x - 8)(3x - 2) = 0
-x - 8 = 0 hoặc 3x - 2 = 0
*) -x - 8 = 0
-x = 8
x = -8
*) 3x - 2 = 0
3x = 2
x = 2/3
Vậy x = -8; x = 2/3
--------------------
27x³ - 54x² + 36x = 9
27x³ - 54x² + 36x - 9 = 0
27x³ - 27x² - 27x² + 27x + 9x - 9 = 0
(27x³ - 27x²) - (27x² - 27x) + (9x - 9) = 0
27x²(x - 1) - 27x(x - 1) + 9(x - 1) = 0
(x - 1)(27x² - 27x + 9) = 0
x - 1 = 0 hoặc 27x² - 27x + 9 = 0
*) x - 1 = 0
x = 1
*) 27x² - 27x + 9 = 0
Ta có:
27x² - 27x + 9
= 27(x² - x + 1/3)
= 27(x² - 2.x.1/2 + 1/4 + 1/12)
= 27[(x - 1/2)² + 1/12] > 0 với mọi x ∈ R
⇒ 27x² - 27x + 9 = 0 (vô lí)
Vậy x = 1
KV
3 tháng 8 2023
A = x² + y²
= x² - 2xy + y² + 2xy
= (x - y)² + 2xy
= 4² + 2.1
= 16 + 2
= 18
B = x³ - y³
= (x - y)(x² + xy + y²)
= (x - y)(x² - 2xy + y² + xy + 2xy)
= (x - y)[(x - y)² + 3xy]
= 4.(4² + 3.1)
= 4.(16 + 3)
= 4.19
= 76
C = x⁴ + y⁴
= (x²)² + (y²)²
= (x²)² + 2x²y² + (y²)² - 2x²y²
= (x² + y²)² - 2x²y²
= (x² - 2x²y² + y² + 2x²y²)² - 2x²y²
= [(x - y)² + 2x²y²]² - 2x²y²
= (4² + 2.1²)² - 2.1²
= (16 + 2)² - 2
= 18² - 2
= 324 - 2
= 322
\(A=\left(x-2\right)^2+\left(x+3\right)^2-2\left(x+1\right)\left(x-1\right).\)
\(A=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(A=x^2-4x+4+x^2+6x+9-2x^2+2\)
\(A=2x+15\)
\(B=\left(x^2-y^2\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(B=\left(x^4-y^4\right)\left(x^4+y^4\right)\left(x^8+y^8\right)\)
\(B=\left(x^8-y^8\right)\left(x^8+y^8\right)\)
\(B=x^{16}-y^{16}\)
VẬY \(B=x^{16}-y^{16}\)