Mathematics, 18.12.2019 06:31 danejac99

Factor 8k3 + 27 by using an identity.
how to do it?

Answers: 3

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Answer from: nika0001

The given expression is factored into (2k+3)(4k^2-6k+9)

Step-by-step explanation:

Given:

The expression to factor is given as:

8k^3+27

We observe that 8 = $2\times 2\times 2=2^3$

Also, $27 = 3\times 3\times 3=3^3$

So, the above expression can be rewritten as:

(2k)^3+3^3

The above expression is of the form a^3+b^3 .

We know that the above identity is factored as:

a^3+b^3=(a+b)(a^2-ab+b^2)

Here, $a=2k\ and\ b=3$

Therefore, the given expression can be factored using the above identity and is factored as:

$(2k)^3+3^3=(2k+3)((2k)^2-(2k)(3)+3^2)\\\\(2k)^3+3^3=(2k+3)(4k^2-6k+9)$

Hence, the given expression is factored into (2k+3)(4k^2-6k+9)

Answer from: Quest

Well in order to lose a pound you would have to burn 1,500 calories. the more calories you burn the more weight you lose. in order to lose 2 pounds you would have to run 4 hours and 28 minutes.

Answer from: Quest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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