Ask Question
1 June, 17:23

Factor the algebraic expression 16a + 36

+2
Answers (1)
  1. 1 June, 20:12
    0
    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)
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “Factor the algebraic expression 16a + 36 ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers