Bài 1

a) x³ - x²z + x²y - xyz

= (x³ - x²z) + (x²y - xyz)

= x²(x - z) + xy(x - z)

= (x² + xy)(x - z)

= x(x + y)(x - z)

b) (x² + 1)² - 4x²

= (x² + 1 + 2x)(x² + 1 - 2x)

= (x² + x + x + 1)(x² - x - x + 1)

= [(x² + x) + (x + 1)].[(x² - x) - (x - 1)]

= [x(x + 1) + (x + 1)].[x(x - 1) - (x - 1)]

= (x + 1)(x + 1)(x - 1)(x - 1)

= (x + 1)²(x - 1)²

c) x² - 10x - 9y² + 25

= (x² - 10x + 25) - 9y²

= (x - 5)² - (3y)²

= (x - 5 - 3y)(x - 5 + 3y)

= (x - 3y - 5)(x + 3y - 5)

d) 4x² - 36x + 56

= 4x² - 36x + 81 - 25

= (4x² - 2.2x.9 + 9²) - 5²

= (2x - 9)² - 5²

= (2x - 9 - 5)(2x - 9 + 5)

= (2x - 14)(2x - 4)

Bài 2.

a) (3x + 4)² - (3x + 1)(3x - 1) = 0

9x² + 12x + 16 - 9x² + 1 = 0

12x + 17 = 0

\(\Rightarrow\) 12x = -17

\(\Rightarrow\) x = \(\dfrac{-17}{12}\)

b) x² - 4x + 4 = 9(x - 2)

x² - 4x + 4 - 9(x - 2) = 0

x² - 4x + 4 - 9x + 18 = 0

x² - 13x + 22 = 0

x² - 2x - 11x + 22 = 0

(x² - 2x) - (11x - 22) = 0

x(x - 2) - 11(x - 2) = 0

(x - 11)(x - 2) = 0

\(\Rightarrow\left\{{}\begin{matrix}x-11=0\\x-2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=11\\x=2\end{matrix}\right.\)

c) x² - 25 = 3x - 15

\(\Rightarrow\) x² - 25 - 3x + 15 = 0

x² - 3x - 10 = 0

x² + 2x - 5x - 10 = 0

(x² + 2x) - (5x + 10) = 0

x(x + 2) - 5(x + 2) = 0

(x - 5)(x + 2) = 0

\(\Rightarrow\left\{{}\begin{matrix}x-5=0\\x+2=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=5\\x=-2\end{matrix}\right.\)

d) (x - 1)³ + 3(x + 1)² = (x² - 2x + 4)(x + 2)

x³ - 3x² + 3x - 1 + 3(x² + 2x + 1) = x³ + 8

x³ - 3x² + 3x - 1 + 3x² + 6x + 3 - x³ - 8 = 0

9x - 6 = 0

\(\Rightarrow\) 9x = 6

\(\Rightarrow\) x = \(\dfrac{2}{3}\)

Bài 3

a) (10x³y - 5x²y² - 25x⁴y³) : (-5xy)

=(-5xy)(-2x² + xy + 5x³y²) : (-5xy)

= -2x² + xy + 5x³y²

b) [15(x - y)⁵ - 9(x - y)⁴ + 12(y - x)²] : (y - x)²

= [15(x - y)⁵ - 9(x - y)⁴ + 12(x - y)²] : (x-y)²

= (x - y)²[15(x - y)³ - 9(x - y)² + 12] : (x - y)²

= 15(x - y)³ - 9(x - y)² + 12

c) (27x³ - y³) : (3x - y)

= (3x - y)(9x² + 3xy + y²) : (3x - y)

= 9x² + 3xy + y²

d) (15x⁴ + 4x³ + 11x² + 14x - 8) : (5x² + 3x - 2)

= (15x⁴ + 15x³ - 11x³ - 11x² + 22x² + 22x - 8x - 8) : (5x² + 3x - 2)

= [ (15x⁴ + 15x³) - (11x³ + 11x²) + (22x² + 22x) - (8x + 8)] : (5x² + 3x - 2)

= [15x³(x + 1) - 11x²(x + 1) + 22x(x + 1) - 8(x + 1)] : (5x² + 3x - 2)

= (15x³ - 11x² + 22x - 8)(x + 1) : (5x² + 3x - 2)

= (15x³ - 6x² - 5x² + 2x + 20x - 8)(x + 1) : (5x² + 3x - 2)

= [(15x³ - 6x²) - (5x² - 2x) + (20x - 8)](x + 1) : (5x² + 3x - 2)

= [3x²(5x - 2) - x(5x - 2) + 4(5x - 2)](x + 1) : (5x² + 3x - 2)

= (3x² - x + 4)(5x - 2)(x + 1) : (5x² + 3x - 2)

= (3x² - x + 4)(5x² + 5x - 2x - 2) : (5x² + 3x - 2)

= (3x² - x + 4)(5x² + 3x - 2) : (5x² + 3x - 2)

= 3x² - x + 4

NHỚ TIK MK NHÉ

trục đối xứng nó cũng giống như đường trung trực đấy bạn ạ

a=1/1x2+1/2x3+....+1/99x100

a=1-1/2+1/2-1/3+....+1/99-1/100

a=1-1/100

a=99/100

b=4/1x3+4/3x5+.....+4/51x53

b=2x(2/1x3+2/3x5+....+2/51x53)

b=2x(1-1/3+1/3-1/5+...+1/51-1/53)

b=2x(1-1/53)

b=2x52/53

b=104/53

đúng tick cho mình nha

tổng độ dài 2 đáy là:

3 + 11 = 14(cm)

vì đường trung bình bằng \(\dfrac{1}{2}\) tổng độ dài 2 đáy (t/chất)

\(\Rightarrow\) độ dài đường trung binh là:

14.\(\dfrac{1}{2}\)= 7 (cm)

NHỚ TIK MK NHÉ

(x - 3)(x + 3) = 0

\(\Rightarrow\) x² - 9 = 0

\(\Rightarrow\) x² = 9

\(\Rightarrow\) x = \(\pm\) 3

cách của mik nhanh hơn nên cho mik 2 tik nhé

Bài 1

a) (x⁵ + 4x³ - 6x²) : 4x²

= 4x²(\(\dfrac{1}{4}\)x³ + x - \(\dfrac{3}{2}\)) : 4x²

= \(\dfrac{1}{4}\)x³ + x - \(\dfrac{3}{2}\)

b) (x³ - 8) : (x² + 2x + 4)

= (x - 2)(x² + 2x + 4) : (x² + 2x + 4)

= x - 2

c) (3x² - 6x) : (2 - x)

= -(6x - 3x²) : (2 - x)

= -3x(2 - x) : (2 - x)

= -3x

d) (x³ + 2x² - 2x - 1) : (x² + 3x + 1)

= [(x³ - 1) + (2x² - 2x)] : (x² + 3x + 1)

= [(x - 1)(x² + x + 1) + 2x(x - 1)] : (x² + 3x + 1)

= (x - 1)(x² + x + 1 + 2x) : (x² + 3x + 1)

= (x - 1)(x² + 3x + 1) : (x² + 3x + 1)

= x - 1

Bài 2

a) (x - 4)² - (x - 2)(x + 2) = 6

x² - 8x + 16 - (x² - 4) = 6

x² - 8x + 16 - x² + 4 = 6

-8x + 20 = 6

\(\Rightarrow\) -8x = - 14

\(\Rightarrow\) x = \(\dfrac{7}{4}\)

b) 9(x + 1)² - (3x - 2)(3x + 2) = 10

9(x² + 2x + 1) - (9x² - 4) = 10

9x² + 18x + 9 - 9x² + 4 = 10

18x + 13 = 10

\(\Rightarrow\) 18x = -3

\(\Rightarrow\) x = \(\dfrac{-1}{6}\)

Nhớ tik mik nha

không lần sau mik ko giúp đâu

AK... có j ko hiểu thì bn cứ bình luận bên dưới

a) (x - 1)³ + 3(x + 1)² = (x² - 2x + 4)(x + 2)

x³ - 3x² + 3x - 1 + 3(x² + 2x+ 1) = x³ + 8

\(\Rightarrow\)x³ - 3x² + 3x - 1 + 3x² + 6x - x³ - 8 = 0

\(\Rightarrow\) 9x - 9 = 0

\(\Rightarrow\) 9x = 9

\(\Rightarrow\) x = 1

b) (2x - 1)(x + 3) - x(3 + 2x) = 26

2x² + 6x - x - 3 - 3x - 2x² = 26

2x - 3 = 26

\(\Rightarrow\) 2x = 29

\(\Rightarrow\) x = 14.5

a) (2x - 3)² - 4(x + 2)(x - 2) - x = 8

4x² - 12x + 9 - 4(x² - 4) - x = 8

4x² - 12x + 9 - 4x² + 16 - x = 8

-13x + 25 = 8

\(\Rightarrow\) -13x = -17

\(\Rightarrow\) x = \(\dfrac{17}{13}\)

b) (3x³ + 6x²) : 3x² + (9x² - 6x) : 0,5x = 9

3x²(x + 2) : 3x² + 3x(3x - 2) : 0,5x = 9

\(\Rightarrow\) x + 2 + 6.(3x - 2) = 9

\(\Rightarrow\) x + 2 + 18x - 12 = 9

\(\Rightarrow\) 19x - 10 = 9

\(\Rightarrow\) 19x = 19

\(\Rightarrow\) x = 1

chúc bn học tốt. nhớ tik mik nhé

a) 2x²y(4x³y - \(\dfrac{1}{2}\)x² + 2)

= 8x⁵y² - x²y + 4x²y

b) (x + 3)(5x - 2)

= 5x² - 2x + 15x - 6

= 5x² + 13x - 6

c) (x + 3)(x - 3) - (x + 6)² + 12

= x² - 9 - (x² - 12x + 36) + 12

= x² - 9 - x² + 12x - 36 + 12

= 12x - 33

chúc bn hok tốt (nhớ tik mik nhé )