\(\left(x^2-2x+3\right)\left(\dfrac{1}{2}x-5\right)\)

\(=\dfrac{1}{2}x^3-x^2+\dfrac{3}{2}x-5x^2+10x-15\)

\(=\dfrac{1}{2}x^3-6x^2+\dfrac{23}{2}x-15\)

\(\left(x^2-2x+3\right)\left(\dfrac{1}{2}x-5\right)\)

\(=\dfrac{1}{2}x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15\)

\(=\dfrac{1}{2}x^3-6x^2+\dfrac{23}{2}x-15\)

\(=\dfrac{1}{2}x^3-5x^2-x^2+10x+\dfrac{3}{2}x-15=\dfrac{1}{2}x^3-6x^2+\dfrac{23}{2}x-15\)

=12x^3−x^2+32x−5x^2+10x−15

Bài 1:

(x² - 8)(x³ + 2x + 4)

= x².x³ + x².2x + x².4 - 8.x³ - 8.2x - 8.4

= x⁵ + 2x³ + 4x² - 8x³ - 16x - 32

= x⁵ - 6x³ + 4x² - 16x - 32

Bài 2

a) A(x) = -5/3 x² + 3/4 x⁴ + 2x - 7/3 x² - 2 + 4x + 1/4 x⁴

= (3/4 x⁴ + 1/4 x⁴) + (-5/3 x² - 7/3 x²) + (2x + 4x) - 2

= x⁴ - 4x² + 6x - 2

b) Bậc của A(x) là 4

Hệ số cao nhất là 1

`1,`

`b,`

`(x^2-8)(x^3+2x+4)`

`= x^2(x^3+2x+4)-8(x^3+2x+4)`

`= x^5+2x^3+4x^2-8x^3-16x-12`

`= x^5-6x^3+4x^2-16x-12`

`2,`

`a,`

`A(x)=-5/3x^2 + 3/4x^4 + 2x - 7/3x^2 - 2 + 4x + 1/4x^4`

`= (3/4x^4+1/4x^4)+(-5/3x^2-7/3x^2)+(2x+4x)-2`

`= x^4-4x^2+6x-2`

`b,`

Bậc của đa thức: `4`

Hệ số cao nhất: `1`.

Mình xp giúp được mỗi câu đầu thôi nha ;-;;;; 2 câu sau mình chưa học, bạn thông cảm ;-;;;.

`a,` \(\text{P(x) =}\)\(2x^3-3x+x^5-4x^3+4x-x^5+x^2-2\)

`P(x)= (2x^3 - 4x^3)-(3x-4x) +(x^5-x^5) +x^2-2`

`P(x)= -2x^3- (-x)+0+x^2-2`

`P(x)=-2x^3+x+x^2-2`

`Q(x)= x^3-x^2+3x+1+3x^2`

`Q(x)= x^3- (x^2-3x^2) +3x+1`

`Q(x)=x^3- (-2x^2)+3x+1`

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

\(=x^3+x^2+2x^2+2x+x+1\)

\(=x^3+3x^2+3x+1\)

b) Ta có: \(\left(x^3-x^2+2x-1\right)\left(5-x\right)\)

\(=5x^3-x^4-5x^2+x^3+10x-2x^2-5+5x\)

\(=-x^4+6x^3-7x^2+15x-5\)

Ta có: \(\left(x-5\right)\left(x^3-x^2+2x-1\right)\)

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

\(=x^4-6x^3+7x^2-15x+5\)

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

\(=x^3+x^2y-3x^2y-3xy^2\)

\(=x^2-2x^2y-3xy^2\)

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

\(=x^3-x^3y-3xy^2\)

\(=x^2-2x^2y-3xy^2\)

Ta có:

(2x – 3) . (x² – 5x + 1)

= 2x. (x² – 5x + 1)  + (-3). (x² – 5x + 1)

= 2x . x² + 2x . (-5x) + 2x . 1 + (-3).x² + (-3).(-5x) + (-3). 1

= 2x³ + (-10x² ) + 2x + (-3x²) + 15x + (-3)

= 2x³ + (-10x² + -3x²) + (2x + 15x) + (-3)

a. \(12^2.3^2.2^3=2^4.3^2.3^2.2^3=2^7.3^4\)

b. \(8^3.3^2.6^3=2^9.3^2.2^3.3^3=2^{12}.3^5\)

c. \(5^{32}.5^2=5^{34}\)

d. \(100^6.2^3=\left(2^2.5^2\right)^6.2^3=2^8.5^8.2^3=2^{11}.5^8\)

e. \(100^2:10^2:5^2=\left(10.5.2\right)^2:10^2:5^2=2^2\)

f. \(121^3-11^2=11^6-11^2=11^2\left(11^4-1\right)\)

cho mình hỏi mũ là gì

\(8^5\cdot2^3=2^{15}\cdot2^3=2^{18}\)