Fully Factorise Algebraic Expression 40n^2 + 32

Learn how to fully factorise the algebraic expression 40n^2 + 32 by finding the greatest common factor of the terms.

Answer

To fully factorise the expression

, we need to find the greatest common divisor (GCD) of the two terms.

Step 1: Find the greatest common factor (GCF) of the coefficients.
The coefficients are

and

The greatest common factor shared by both

and

Step 2: Factor out the GCF from the expression.
We divide each term of the expression by

Now, we write the expression as the product of the GCF and the remaining terms:

Step 3: Check if the expression inside the parentheses can be factorised further.
The expression inside the parentheses is

. Since

and

have no common factors other than

, and it is a sum of squares (not a difference of squares), it cannot be factorised further using rational numbers.

Final Answer:
The fully factorised form is:

Question