SOLUTION: Factorise: #1 a2 + 6ab + 9b2 - 1 PLEASE NOTE THAT IN THE QUESTION a AND b ARE NOT MULTIPLYING BY 2, BUT BOTH HAVE SQUARES i.e. (a)square + 6ab + 9(b)square - 1

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Question 91731: Factorise:
#1 a2 + 6ab + 9b2 - 1
PLEASE NOTE THAT IN THE QUESTION a AND b ARE NOT MULTIPLYING BY 2, BUT BOTH HAVE SQUARES i.e. (a)square + 6ab + 9(b)square - 1
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Factorise:
a%5E2%2B6ab%2B9b%5E2-1 Rewrite this as:
%28a%5E2%2B6ab%2B9b%5E2%29-1 Factorise the parentheses.
%28a%2B3b%29%28a%2B3b%29-1 which can be written as:
%28a%2B3b%29%5E2-1 Now you have a difference of two squares which can be factored...oops - factorised thus:
A%5E2-B%5E2+=+%28A%2BB%29%28A-B%29 Applying this to your problem,we get:
%28a%2B3b%2B1%29%28a%2B3b-1%29
Check the answer by multiplying the two factors.
Simplify this.
a%5E2%2B3ab%2B3ab%2B9b%5E2-1 Combine like-terms.
a%5E2%2B6ab%2B9b%5E2-1 ...your original expression.