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3 years ago

What is the product? 3x^5 (2x^2+4x+1)

Mathematics

2 answers:

s2008m [1.1K]3 years ago

8 0

Answer:

The product of the given polynomial $3x^5(2 x^2+4x+1)$ is $6x^7+12x^6+3x^5$

Step-by-step explanation:

Given: Polynomial $3x^5(2 x^2+4x+1)$

We have to find the product of the given polynomial $3x^5(2 x^2+4x+1)$

Consider the given polynomial $3x^5(2 x^2+4x+1)$

Apply distributive rule, $a(b+c)=ab+ac$

Multiply $3x^5$ with each term in brackets, we have,

$=3x^5\cdot \:2x^2+3x^5\cdot \:4x+3x^5\cdot \:1$

$=3\cdot \:2x^5x^2+3\cdot \:4x^5x+3\cdot \:1\cdot \:x^5$

Apply exponent rule, $a^b\cdot \:a^c=a^{b+c}$

Simplify, we have,

$=6x^7+12x^6+3x^5$

Thus, The product of the given polynomial $3x^5(2 x^2+4x+1)$ is $6x^7+12x^6+3x^5$

almond37 [142]3 years ago

5 0

the answer is C.) 6x^7...

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Read 2 more answers

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zhannawk [14.2K]

Part A.
y=4x+3

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11=4x+3
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2 years ago

Helpp!! Simplify : [( 4 1/6 + 2 1/3 ) ÷ 4 1/3 ] - 1 1/2

Nadusha1986 [10]

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{0}}}}}$

Step-by-step explanation:

$\sf{ [ (4 \frac{1}{6} + 2 \frac{1}{3} ) \div 4 \frac{1}{3}] - 1\frac{1}{2} }$

Convert the mixed numbers into improper fraction

$\longrightarrow{ \sf{ [ ( \frac{25}{6} + \frac{7}{3} ) \div \frac{13}{3}] - \frac{3}{2}}}$

Add the fractions : 25 / 6 and 7 / 3

While performing addition or subtraction of unlike fractions, you have to express the given fractions into equivalent fractions of common denominator and add or subtract as we do with like fraction.

To do so, first take the L.C.M of 6 and 3 which results to 6

$\longrightarrow\sf{ [( \frac{25 + 7 \times 2}{6} ) \div \frac{13}{3} ] - \frac{3}{2}}$

$\longrightarrow{ \sf{ [( \frac{25 + 14}{6} ) \div \frac{13}{3} ] - \frac{3}{2} }}$

$\longrightarrow{ \sf{ [ \frac{39}{6} \div \frac{13}{3}] - \frac{3}{2} }}$

Multiply the dividend by the reciprocal of the divisor.

Reciprocal of any number or fraction can be obtained by interchanging the position of numerator and denominator

$\longrightarrow{ \sf{ [ \frac{39}{6} \times \frac{3}{13} ] - \frac{3}{2}}}$

To multiply one fraction by another, multiply the numerators for the numerator and multiply the denominators for its denominator and reduce the fraction obtained after multiplication into lowest term

$\longrightarrow{ \sf{ [ \frac{39 \times 3}{6 \times 13} ] - \frac{3}{2}}}$

$\longrightarrow{ \sf{ [ \frac{117}{78} ] - \frac{3}{2} }}$

$\longrightarrow{ \sf{ \frac{3}{2} - \frac{3}{2} }}$

While performing the addition or subtraction of like fractions , you just have to add or subtract the numerator respectively in which the denominator is retained same

$\longrightarrow{ \sf{ \frac{3 - 3}{2} }}$