Answer:
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)
