Question

Factor completely: 27x2−75y2 Question 1 options: −3(−27x2−25y2) −3(3x+5y)2 3(3x−5y)2 3(3x+5y)(3x−5y)

Answer 1

The fully factored form of the expression 27x^2−75y^2 is 3(3x + 5y)(3x − 5y), using the difference of squares factoring formula.

Step-by-step explanation:

To factor the expression 27x^2−75y^2 completely, we recognize it as a difference of squares, which is a special factoring formula: a^2−b^2 = (a+b)(a−b). Applying this to our expression, we get:

27x^2−75y^2 = (3x)^2−(5y)^2

Now we can factor it as the product of two binomials:

(3x + 5y)(3x − 5y)

The fully factored form of the given expression is 3(3x + 5y)(3x − 5y). We introduced a factor of 3 to correctly represent the coefficient 27 as 33 and 75 as 3×25.

Answer 2

3(3x-5y) (3x+5y)

Step-by-step explanation:

27x^2−75y^2

Factor out a 3

3(9x^2 -25y^2)

This is the difference of squares

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

a^2 = 9x^2 so a =3x

b^2 = 25y^2 =5y

3(9x^2 -25y^2) = 3(3x-5y) (3x+5y)