How do I factor 45b2 plus 150bd plus 125d2?

Answer 1

45bb+150bd+125dd

Steps:

1. Factor out common terms

45bb+150bd+125dd

5(9bb+30bd+25dd)

2. Multiply coefficients of first and third terms:

9*25=225

3. Factor product of first and third terms, choose factors whose sum is the second term(30):

225=3*3*5*5

=3*75

=5*45

=15*15

4. Rewrite polynomial:

5(9bb+30bd+25dd)

5(9bb+15bd+15bd+25dd)

5. Factor sets of terms (first and second, third and fourth):

5(9bb+15bd+15bd+25dd)

5(3b(3b+5d)+5d(3b+5d)

6. Combine like terms:

5(3b+5d)(3b+5d)

7. Combine like terms:

5(3b+5d)**2