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# algebra

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1. Simplify 12a3b2 ÷ 4ab−2.

kazza1969  May 7, 2015

#1
+18829
+15

Simplify 12a3b2 ÷ 4ab−2.

$$\\\small{\text{  \begin{array}{rcl} \dfrac{ 12\cdot a^3 \cdot b^2 }{ 4 \cdot a \cdot b^{-2} } \\\\ =\dfrac{ 12 } {4} \cdot \dfrac{ a^3 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot 4 } {4} \cdot \dfrac{ a\cdot a^2 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot \not{4} } {\not{4}} \cdot \dfrac{ \not{a}\cdot a^2 }{ \not{a} } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot b^{2-(-2) } \\\\ = 3\cdot a^2 \cdot b^{2+2} \\\\ = 3\cdot a^2 \cdot b^4 \end{array} }}$$

heureka  May 7, 2015
Sort:

#1
+18829
+15

Simplify 12a3b2 ÷ 4ab−2.

$$\\\small{\text{  \begin{array}{rcl} \dfrac{ 12\cdot a^3 \cdot b^2 }{ 4 \cdot a \cdot b^{-2} } \\\\ =\dfrac{ 12 } {4} \cdot \dfrac{ a^3 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot 4 } {4} \cdot \dfrac{ a\cdot a^2 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot \not{4} } {\not{4}} \cdot \dfrac{ \not{a}\cdot a^2 }{ \not{a} } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot b^{2-(-2) } \\\\ = 3\cdot a^2 \cdot b^{2+2} \\\\ = 3\cdot a^2 \cdot b^4 \end{array} }}$$

heureka  May 7, 2015
#2
+91462
0

Another great answer Heureka :)

I have a couple of questions about your coding Heureka

1)  I have trouble remembering \cdot because it means nothing to me.  Do you think the c stands for centre ?

Are there any other types of dots that you can have?

2)   What is  \text{for? What does it do, I see no text. 3) You have your alignment as rcl right, centre, left but there are no & symbols. I experimented with leaving out the cl and it looked just the same - do they do anything? Thank you :) $$\\\small{\text{\begin{array}{rcl}\dfrac{ 12\cdot a^3 \cdot b^2 }{ 4 \cdot a \cdot b^{-2} } \\\\ =\dfrac{ 12 } {4} \cdot \dfrac{ a^3 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot 4 } {4} \cdot \dfrac{ a\cdot a^2 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ =\dfrac{ 3\cdot \not{4} } {\not{4}} \cdot \dfrac{ \not{a}\cdot a^2 }{ \not{a} } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot \dfrac{ b^2 }{ b^{-2} } \\\\ = 3\cdot a^2 \cdot b^{2-(-2) } \\\\ = 3\cdot a^2 \cdot b^{2+2} \\\\ = 3\cdot a^2 \cdot b^4 \end{array}}}$$ \\\small{\text{\begin{array}{rcl}\dfrac{ 12\cdot a^3 \cdot b^2 }{ 4 \cdot a \cdot b^{-2} } \\\\

=\dfrac{ 12 } {4} \cdot \dfrac{ a^3 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\

=\dfrac{ 3\cdot 4 } {4} \cdot \dfrac{ a\cdot a^2 }{ a } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\

=\dfrac{ 3\cdot \not{4} } {\not{4}} \cdot \dfrac{ \not{a}\cdot a^2 }{ \not{a} } \cdot \dfrac{ b^2 }{ b^{-2} } \\\\

= 3\cdot a^2 \cdot \dfrac{ b^2 }{ b^{-2} } \\\\

= 3\cdot a^2 \cdot b^{2-(-2) } \\\\

= 3\cdot a^2 \cdot b^{2+2} \\\\

= 3\cdot a^2 \cdot b^4 \end{array}$} Melody May 7, 2015 #3 +91462 0 Hi Heureka, I added some questions for you that you may not have seen (it was an edit) If you get a chance could you take a look please? Melody May 7, 2015 #4 +18829 +5 I have trouble remembering \cdot because it means nothing to me. Do you think the c stands for centre ? Are there any other types of dots that you can have? horizontal, center (c): \cdots $$A_{11}\cdots A_{1n}$$ horizontal, down: \ldots $$A \ldots A$$ Example: _pF_q(a_1, \ldots, a_p; c_1, \ldots, c_q; z) = \sum_{n=0}^\infty \frac{(a_1)_n \cdots (a_p)_n}{(c_1)_n \cdots (c_q)_n} \frac{z^n}{n!} $$_pF_q(a_1, \ldots, a_p; c_1, \ldots, c_q; z) = \sum_{n=0}^\infty \frac{(a_1)_n \cdots (a_p)_n}{(c_1)_n \cdots (c_q)_n} \frac{z^n}{n!} \,$$ diagonal (d) : \ddots $$\ddots$$ vertical(v) : \vdots $$\vdots$$ ### Dots The most common dot symbols used in math notation are available in LaTeX as well. NameSymbolCommand Middot / Centered dot $$\cdot$$ \cdot Horizontal Dots / Centered dots $$\cdots$$\cdots Vertical Dots $$\vdots$$\vdots Diagonal Dots $$\ddots$$\ddots Lower Dots $$\ldots$$ \ldots Example: ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ 111 000 0 000 ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ $$\begin{bmatrix} 1 & 0 & \cdots & 0\\ 1 & 0 & \cdots & 0\\ \vdots & \vdots & \ddots & \vdots \\ 1 & 0 & 0 & 0 \end{bmatrix}$$ \begin{bmatrix} 1 & 0 & \cdots & 0\\ 1 & 0 & \cdots & 0\\ \vdots & \vdots & \ddots & \vdots \\ 1 & 0 & 0 & 0 \end{bmatrix} double (d): \ddot $$\ddot{a}$$ single: \dot $$\dot{a}$$ heureka May 7, 2015 #5 +91462 0 WOW there are a lot of dot commands. Thanks Heureka. wWhat about your used of \text There doesn't seem to be any text there so what is it for? Melody May 7, 2015 #6 +18829 +5 What is \text{$   for?   What does it do, I see no text.

big         \small{mathe-Modus}}     :             $$\small{mathe-Modus}}$$

small      \small{\text{text-Modus}} :            $$\small{\text{text-Modus}}$$

small - italic    \small{\text{$mathe-Modus-italic$}} :     $$\small{\text{mathe-Modus-italic}}$$

heureka  May 7, 2015
#7
+18829
+5

You have your alignment as rcl   right, centre, left  but there are no & symbols.

I experimented with leaving out the cl  and it looked just the same - do they do anything?

they do nothing, only placeholder!

heureka  May 7, 2015
#8
+91462
0

Thank you Heureka

Melody  May 7, 2015

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