3 years ago

Expand and simplify (x + 3)(x-4)

Mathematics

2 answers:

Hunter-Best [27]3 years ago

5 0

Answer:

2x -1

Step-by-step explanation:

x*x =2x 3-4 =-1

2x+-4

sweet [91]3 years ago

4 0

Answer: x^2x-12 (by the way ^2 is a square)

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kirill [66]

Answer:

$a(x)=\dfrac{1}{1+2x}$

Step-by-step explanation:

The generating function a(x) produces a power series ...

$a(x)=a_0+a_1x+a_2x^2+a_3x^3+\dots$

where the coefficients are the elements of the given sequence.

We observe that the given sequence has the recurrence relation ...

$a_0=1;a_n=-2a_{n-1} \quad\text{for n $>$ 0}$

This can be rearranged to ...

$a_n+2a_{n-1}=0$

We can formulate this in terms of a(x) as follows, then solve for a(x).

$\sum\limits^{\infty}_{n=1} {a_{n}x^n} =a(x)-a_0 \quad\text{and}\\\\\sum\limits^{\infty}_{n=1} {2a_{n-1}x^n} =(2x)a(x) \quad\text{so}\\\\\sum\limits^{\infty}_{n=1} {(a_n+2a_{n-1})x^n}=0=a(x)-a_0+2xa(x)\\\\a(x)=\dfrac{a_0}{1+2x}=\dfrac{1}{1+2x}$

The generating function is ...

a(x) = 1/(1+2x)

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