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Katen [24]
3 years ago
7

12a^3b^2 +18a²b^2 – 12ab^2 Factor completely

Mathematics
1 answer:
AleksAgata [21]3 years ago
4 0

The factorization of 12a^3b^2 +18a²b^2 – 12ab^2 is 6 a b^{2}(a+2)(2 a-1)

<u>Solution:</u>

Given, expression is 12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}

We have to factorize the given expression completely.

Now, take the expression

12 a^{3} b^{2}+18 a^{2} b^{2}-12 a b^{2}

Taking b^2 as common term,

b^{2}\left(12 a^{3}+18 a^{2}-12 a\right)

Taking "a" as common term,

b^{2}\left(a\left(12 a^{2}+18 a-12\right)\right)

Taking "6" as common term,

b^{2}\left(a\left(6\left(2 a^{2}+3 a-2\right)\right)\right)

Splitting "3a" as "4a - a" we get,

b^{2}\left(a\left(6\left(2 a^{2}+4 a-a-2\right)\right)\right)

\begin{array}{l}{b^{2}(a(6(2 a(a+2)-1(a+2))))} \\\\ {b^{2}(a(6((a+2) \times(2 a-1))))} \\\\ {6 a b^{2}(a+2)(2 a-1)}\end{array}

Hence, the factored form of given expression is 6 a b^{2}(a+2)(2 a-1)

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Answer: Ali would need to drive 350 miles for the two plans to cost the same.

Step-by-step explanation:

This question can be solved by creating two equations using the information supplied in the question and then solving these simultaneously.

Let the cost be C.

Let the number of miles be M.

Let the initial payment be i.

Let the rate per mile driven be R.

Plan 1:

C = i+R×M

C = 70+0.60M ... equation 1

Plan 2:

C = i+R×M

C = 0+0.80M

C = 0.80M ...equation 2

Substituting equation 2 into equation 1:

0.80M = 70+0.60M

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5 0
3 years ago
Please answer both with work,please use a paper and picture, thanks ​
Irina-Kira [14]

Answer:

a.  $ \frac{\textbf{17}}{\textbf{4}} $

b.  $ \frac{\textbf{3}}{\textbf{8}} $

Step-by-step explanation:

a. $ \textbf{3} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{1}\frac{\textbf{1}}{\textbf{4}} $

A mixed fraction of the form $ a\frac{x}{y} = a + \frac{x}{y} $

$ \therefore 3 + 1\frac{1}{4} = 3 + 1 + \frac{1}{4} $

$ = 4 + \frac{1}{4} $

$ = \frac{\textbf{17}}{\textbf{4}} $

b. $ \textbf{2} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{1}\frac{\textbf{5}}{\textbf{8}} $

A mixed fraction of the form $ -c\frac{a}{b} = - c - \frac{a}{b} $

$ \therefore 2 - 1\frac{5}{8} = 2 - 1 - \frac{5}{8} $

$ = 1 - \frac{5}{8} $

$ = \frac{8 - 5}{8} $

$ = \frac{\textbf{3}}{\textbf{8}} $

Hence, the answer.

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Given the equation:

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We will use the following rule to find the solution to the equation:

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So,

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So, the answer will be option B) x = -1/2, -2/3

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