Factor the algebraic expression 16a + 36

4 • (2a + 3b) • (2a - 3b)

Step-by-step explanation:

Step 1:

Equation at the end of step 1:

(16 • (a2)) - (22•32b2)

Step 2:

Equation at the end of step 2:

24a2 - (22•32b2)

Step 3:

Step 4:

Pulling out like terms:

4.1 Pull out like factors:

16a2 - 36b2 = 4 • (4a2 - 9b2)

Trying to factor as a Difference of Squares:

4.2 Factoring: 4a2 - 9b2

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 4 is the square of 2

Check : 9 is the square of 3

Check : a2 is the square of a1

Check : b2 is the square of b1

Factorization is : (2a + 3b) • (2a - 3b)

Final result:

4 • (2a + 3b) • (2a - 3b)