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myrzilka [38]
3 years ago
9

TIMED PLEASE HURRY HELP WITH 2 EASY QUESTIONS

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
8 0
<h2>                         Question # 1</h2><h2>Which statements are true?</h2><h2 /><h3><u>Analyzing and solving the first statement:</u></h3>
  • 4g^2-g=g^2\left(4-g\right)

Solving the expression

4g^2-g

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

g^2=gg

So,

4gg-g

\mathrm{Factor\:out\:common\:term\:}g

g\left(4g-1\right)

So,

4g^2-g:\quad g\left(4g-1\right)

Therefore, the statement 4g^2-g=g^2\left(4-g\right) is NOT CORRECT.

<h3><u>Analyzing and solving the second statement:</u></h3>
  • 35g^5-25g^2=\:5g^2\left(7g^3-5\right)

Solving the expression

35g^5-25g^2

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

g^5=g^3g^2

So,

35g^3g^2-25g^2

\mathrm{Rewrite\:}25\mathrm{\:as\:}5\cdot \:5

\mathrm{Rewrite\:}35\mathrm{\:as\:}5\cdot \:7

5\cdot \:7g^3g^2-5\cdot \:5g^2

\mathrm{Factor\:out\:common\:term\:}5g^2

5g^2\left(7g^3-5\right)

So,

35g^5-25g^2=\:5g^2\left(7g^3-5\right)

Therefore, the statement 35g^5-25g^2=\:5g^2\left(7g^3-5\right) is CORRECT.

<h3><u>Analyzing and solving the third statement:</u></h3>
  • 24g^4+18g^2=\:6g^2\left(4g^2+3g\right)
<h3 />

Solving the expression

<h3>24g^4+18g^2</h3><h3>24g^2g^2+18g^2</h3><h3>\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3</h3><h3>\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4</h3><h3>6\cdot \:4g^2g^2+6\cdot \:3g^2</h3><h3>\mathrm{Factor\:out\:common\:term\:}6g^2</h3><h3>6g^2\left(4g^2+3\right)</h3>

So,

<h3>24g^4+18g^2=6g^2\left(4g^2+3\right)</h3>

Therefore, the statement 24g^4+18g^2=\:6g^2\left(4g^2+3g\right)  is CORRECT.

<h3><u>Analyzing and solving the fourth statement:</u></h3>
  • 9g^3+12=\:3\left(3g^3+4\right)

Solving the expression

9g^3+12

\mathrm{Rewrite\:}12\mathrm{\:as\:}3\cdot \:4

\mathrm{Rewrite\:}9\mathrm{\:as\:}3\cdot \:3

3\cdot \:3g^3+3\cdot \:4

\mathrm{Factor\:out\:common\:term\:}3

3\left(3g^3+4\right)

So,

9g^3+12=\:3\left(3g^3+4\right)

Therefore, the statement 9g^3+12=\:3\left(3g^3+4\right) is CORRECT.

<h2>                         Question # 2</h2><h2>Which expressions are completely factored?</h2>

<u>Solving first expression</u>

Considering the expression

  • 30a^6-24a^2

30a^6-24a^2

30a^4a^2-24a^2

\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4

\mathrm{Rewrite\:}30\mathrm{\:as\:}6\cdot \:5

6\cdot \:5a^4a^2-6\cdot \:4a^2

\mathrm{Factor\:out\:common\:term\:}3a^2

3a^2\left(10a^4-8\right)

Thus, the expression 30a^6-24a^2=3a^2\left(10a^4-8\right)\: is completely factored.

<u>Solving second expression</u>

Considering the expression

  • 12a^3-8a

12a^3-8a

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

a^3=a^2a

So,

12a^2a-8a

\mathrm{Rewrite\:}8\mathrm{\:as\:}4\cdot \:2

\mathrm{Rewrite\:}12\mathrm{\:as\:}4\cdot \:3

4\cdot \:3a^2a-4\cdot \:2a

\mathrm{Factor\:out\:common\:term\:}4

4\left(3a^3-2a\right)

Thus, the expression 12a^3-8a=\:4\left(3a^3-2a\right) is completely factored.

<u>Solving third expression</u>

  • 16a^5-20a^3\:\:\:\:\:\:\:\:\:\:\:\:

16a^5-20a^3

\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c

a^5=a^2a^3

So,

16a^2a^3-20a^3

\mathrm{Rewrite\:}20\mathrm{\:as\:}4\cdot \:5

\mathrm{Rewrite\:}16\mathrm{\:as\:}4\cdot \:4

4\cdot \:4a^2a^3-4\cdot \:5a^3

\mathrm{Factor\:out\:common\:term\:}4a^3

4a^3\left(4a^2-5\right)

Thus, the expression 16a^5-20a^3\:=4a^3\left(4a^2-5\right) is completely factored.

<u>Solving fourth expression</u>

  • 24a^4+18

24a^4+18

\mathrm{Rewrite\:}18\mathrm{\:as\:}6\cdot \:3

\mathrm{Rewrite\:}24\mathrm{\:as\:}6\cdot \:4

6\cdot \:4a^4+6\cdot \:3

\mathrm{Factor\:out\:common\:term\:}6

6\left(4a^4+3\right)

Thus, the expression 24a^4+18=6\left(4a^4+3\right) is completely factored.

Keywords: expression, factoring

Learn more about expression factoring from brainly.com/question/14051207

#learnwithBrainly

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