What is the LCD of 7(y+2) and y?

1 Answer
Jan 25, 2018

7y^2 + 14y7y2+14y

Explanation:

To find the LCD of regular numbers, you use the following steps:

"Write out the prime factorizations of all of the numbers"Write out the prime factorizations of all of the numbers

"For each prime factor, determine which"For each prime factor, determine which
"number has the highest power of that factor"number has the highest power of that factor

"Multiply together all of the"Multiply together all of the ""highest"highest" "powers of factors to get the LCD"powers of factors to get the LCD

Working with polynomials like this is not much different. The only real difference you'll see here is that some of our prime factors have variables in them, but they're still prime factors because they're as simple as we can get them.

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So, let's find the LCD. Our two numbers are yy and 7(y+2)7(y+2)

Prime factorizations:

7 xx (y+2)7×(y+2)
yy

The factor color(blue)77 occurs the most in the first term, where it occurs color(red)11 time, so we will multiply color(blue)7^color(red)171 into our LCD.

The factor color(orange)yy occurs the most in the second term, where it occurs color(red)11 time, so we will multiply color(orange)y^color(red)1y1 into our LCD.

The factor color(limegreen)((y+2))(y+2) occurs the most in the first term, where it occurs color(red)11 time, so we will multiply color(limegreen)((y+2))^color(red)1(y+2)1 into our LCD.

Therefore, our LCD is:

7^1 xx y^1 xx (y+2)^171×y1×(y+2)1

7y(y+2)7y(y+2)

7y^2 + 14y7y2+14y

Final Answer