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)

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)

idk

step-by-step explanation: