Question

What is (16.72 - 81) in factored form?

a) (4.1)^2 - (9)^2
b) (4.1 - 9)(4.1 + 9)
c) (4.1 + 9)^2
d) (4.1)^2 + (9)^2

What is 16x^2 - 81 in factored form?

a) (4x + 9)(4x - 9)
b) (4x - 9)(4x + 9)
c) 4x^2 - 9^2
d) 4x + 9^2

Answer 1

The factored form of (16.72 - 81) is (4.1 + 9)(4.1 - 9), and the factored form of 16x^2 - 81 is (4x + 9)(4x - 9).

Step-by-step explanation:

The first part of the student's question is asking what is the factored form of the expression (16.72 - 81), which is a difference of squares. The difference of squares can be factored using the formula a^2 - b^2 = (a + b)(a - b). We can see that 16.72 can be written as (4.1)^2 and 81 can be written as (9)^2, making the factored form (4.1 + 9)(4.1 - 9), which corresponds to option b).

The second part of the student's question asks for the factored form of 16x^2 - 81. This is also a difference of squares, following the same pattern as above, can be factored as (4x)^2 - (9)^2 = (4x + 9)(4x - 9), which corresponds to option a).