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2 years ago

11

50a3b-8ab factor the expression completely. part a: factor out the gcf (5 points) part b: factor the difference of perfect squar

es (5 points)

1 answer:

dem82 [27]2 years ago

8 0

Answer:

Step-by-step explanation:

50a³b = 2⋅5²a³b

8ab = 2³ab

GCF = 2ab

50a³b - 8ab = 2ab(5²a² - 2²)

5²a² - 2² = (5a - 2)(5a + 2)

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3 years ago

Write 0.216 as a rational number in lowest terms

lozanna [386]

Answer:

$=\frac{27}{125}$

Step-by-step explanation:

$0.216$

$\mathrm{Multiply\:and\:divide\:by\:10\:for\:every\:number\:after\:the\:decimal\:point.}$

$\mathrm{There\:are\:}3\mathrm{\:digits\:to\:the\:right\:of\:the\:decimal\:point,\:therefore\:multiply\:and\:divide\:by\:}1000$

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$\mathrm{The\:GCD\:of\:}a,\:b\mathrm{\:is\:the\:largest\:positive\:number\:that\:divides\:both\:}a\mathrm{\:and\:}b\mathrm{\:without\:a\:remainder}$

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$=2\cdot \:2\cdot \:2\cdot \:3\cdot \:3\cdot \:3$

$2,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}$

$=2\cdot \:2\cdot \:2\cdot \:5\cdot \:5\cdot \:5$

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$=2\cdot \:2\cdot \:2$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2\cdot \:2=8$

$=8$

$=\frac{8\cdot \:27}{8\cdot \:125}$

$\mathrm{Cancel\:the\:common\:factor:}\:8$

$=\frac{27}{125}$

Hence, the correct answer is $=\frac{27}{125}$

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2 years ago

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