Which expression is equivalent to 16 - 4x^2?

Step-by-step explanation:

STEP

1

:

Equation at the end of step 1

 16 -  22x2

STEP

2

:

STEP

3

:

Pulling out like terms

3.1     Pull out like factors :

  16 - 4x2  =   -4 • (x2 - 4)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  x2 - 4  

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 :  x2  is the square of  x1  

Factorization is :       (x + 2)  •  (x - 2)  

Final result :

 -4 • (x + 2) • (x - 2)

(4 - 2x)(4 + 2x)

Step-by-step explanation:

16 - 4x² ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

16 - 4x²

= 4² - (2x)²

= (4 - 2x)(4 + 2x) ← in factored form

300pi

step-by-step explanation: