Respuesta :
The equivalent expression for 16x^4 -64 is 16(x^{2} +2)(x^{2} -2).
What is a polynomial equation?
A polynomial equation is a sum of constants and variables. A polynomial is an expression consisting of indeterminate's (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
For the given situation,
The expression is 16x^4 -64.
⇒ [tex]16x^{4} -64[/tex]
⇒ [tex]16(x^{4}-64 )[/tex]
⇒ [tex]16((x^{2} )^{2}-2^{2} )\\[/tex]
we know that [tex]a^{2}-b^{2}=(a+b)(a-b)[/tex]
⇒ [tex]16(x^{2} +2)(x^{2} -2)[/tex]
Hence we can conclude that the equivalent expression for 16x^4 -64 is 16(x^{2} +2)(x^{2} -2).
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