The equivalent expression of 25 - 64 are "a), b) and c)"
The given expression is:
25 - 64
To find, the equivalent expressions are:
a) 25 + 40x - 40x - 64
= 25 - 64, is the equivalent expression.
b) 25 + 13x - 13x - 64
= 25 - 64, is the equivalent expression.
c) (5 + 8)(5 - 8)
Using the algebraic identity,
(a + b)(a - b) =
=
= 25 - 64, is the equivalent expression.
d) ( + 13)( - 13)
Using the algebraic identity,
(a + b)(a - b) =
=
= - 169, is not a equivalent expression.
e)
Using the algebraic identity,
, is not a equivalent expression.
∴ The equivalent expression of 25 - 64 are "a), b) and c)".
Answer: option A, B, C are equivalent to [tex]25x^4-64[/tex].
We check each option by simplifying:
A) [tex]25x^4 + 40x - 40x - 64 = 25x^4-64[/tex].
B) [tex]25x^4 + 13x - 13x - 64 = 25x^4-64[/tex]
C) [tex](5x^2 + 8)(5x^2 - 8)=(5x^2)^2-8^2=25x^4-64[/tex]
D) [tex](x^2 + 13)(x^2 - 13)=(x^2)^2-13^2=x^4-169[/tex]
E) [tex](5x^2 - 8)^2=(5x^2)^2-2(5x^2)(8)+8^2=25x^4-80x^2+64[/tex].
So option A, B, C are equivalent to [tex]25x^4-64[/tex].
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