Question

Which expressions are equivalent to 25x^4–64? select three options.

a. 25x^4+40x–40x–64

b. 25x^4+13x–13x–64

c. (5x^2+8)(5x^2–8)

d. (x^2+13)(x^2–13)

e. (5x^2–8)^2

Answer 1

Answer: it’s A, B,C

Explanation:

Answer 2

The equivalent expression of 25
`x^4` - 64 are "a), b) and c)".

Explanation:

The given expression is:

25
`x^4` - 64

To find, the equivalent expressions are:

a) 25
`x^4` + 40x - 40x - 64

= 25
`x^4` - 64, is the equivalent expression.

b) 25
`x^4` + 13x - 13x - 64

= 25
`x^4` - 64, is the equivalent expression.

c) (5
`x^2` + 8)(5
`x^2` - 8)

Using the algebraic identity,

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

=
`(5x^2)^2-8^2`

= 25
`x^4` - 64, is the equivalent expression.

d) (
`x^2` + 13)(
`x^2` - 13)

Using the algebraic identity,

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

=
`(x^2)^2-13^2`

=
`x^4` - 169, is not a equivalent expression.

e)
`(5x^2-8)^2`

Using the algebraic identity,

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

`= (5x^2)^(2) -2(5x^2)(8)+8^2`

`= 25x^4 -80x^2+64`, is not a equivalent expression.

∴ The equivalent expression of 25
`x^4` - 64 are "a), b) and c)".