I need help in factoring

Question

I am totally lost in factoring and when I go to put the equation in for 2y to the third power plus 6y to the second power it doesn't show up.  How do I put in the exponent if its more than to the second power?

I need help in 6y^ + 2y to the third power factored out.

Answer 1

Which question is right  (2y)^3+(6y)^2    or 2y^3+6y^2 ?

To factor this (2y)^3+(6y)^2 =  2^3 y^3+3^2 2^2 y^2 =  2^2 y^2 (2y+3^2 ) =  4y^2 (2y+9)

2y^3 +6y^2 answered by Nataliya

 

 

Answer 2

When using a calculator, you must use the "hat" sign in (^). So, it will look like this: 2y^3+6^2

This will help you with that way. 

 

Factoring: Can be tricky. When factoring, you must think of the whole numbers separate from the exponents.

With the whole numbers you are going to look for a common multiple. (A number that can go into all whole numbers in an equation). In this case 2 and 6. We find that 2 is a common multiple. We are going to divide each number by the common multiple and write it as if it would need to be multiplied back in.

Example: 2(1+3)

Now, we can look at the exponents.

With exponents, we will find the lowest exponent, put it on the outside of the parentheses and subtract it from all exponents, leaving the remainder inside the parentheses.

In this case y^3+y^2

Example: y^2(y^1+0), note the zero in this case is to just hold the place, usually you would place a one there in order to multiply it back out.

Now let's put the whole numbers and exponents together.

2(1+3)

y^2(y+0), note y with no exponent is understood to be to the first power.

____________

2y^2(y+3), note y standing alone is understood to be 1y 

When multiplied back together, you have: 2y^2 * y + 2y^2 * 3 = 2y^3+6y^2

Whole number multiply together, exponents add together.

When factoring you do the opposite, divide and subtract.

 

 

Answer 3

aⁿ
"a"  is base
"n"  is exponent
Some properties of exponent with the same base:
a⁰ = 1
a^m · aⁿ = a^m+n
a^m ÷ aⁿ = a^{m - n} 
ab ± ac = a(b ± c) - distributive property of multiplication.
~~~~~~~~
2y³ + 6y² = 2 · y · y · y + 2 · 3 · y · y
The common factors for each term of expression are "2", "y" and "y" or " 2y² " 
Let's use distributive property of multiplication and move common factors out of parentheses 
           2y³           6y²    
2y² (  ———  +  ———  ) =
           2y²           2y² 

2y² [(2/2) y^{3 - 2} + (6/2) y^{2 - 2} ] = 

2y²(y + 3)