Question

3(x^4-256)÷(x^2+16)​

Answer 1

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Answer 2

The answer of this question is $3(x+4)(x-4)$.

Step-by-step explanation:

We are given,

$3(x^{4} -256)\div(x^{2} +16)$

We have to divide $3(x^{4} -256)$ by $(x^{2} +16)$ and get the answer.

• Formula used,

$(a^{2} -b^{2} )=(a+b)(a-b)$

we use this above formula to solve question.

• Solving given equation,

We have to solve numerator separately to simplify the term.

our numerator is  $3(x^{4} -256)$ .

To simplify numerator we make it as similar to our formula for example we can write $x^{4}$  as  $(x^{2} )^{2}$  just like that we can write $256$ as $(16 )^{2}$ then we get,

$3[(x^{2} )^{2} -(16)^{2} ]$

then by using formula

$(a^{2} -b^{2} )=(a+b)(a-b)$

we can write numerator as,

$3[(x^{2} )^{2} -(16)^{2} ]$

$= 3[(x^{2} +16)(x^{2} -16)]$

as here the values of a and b are

$a=x^{2}$  and $b=16$.

• Division of $3(x^{4} -256)\div(x^{2} +16)$

by using simplified numerator for division we get,

$\frac{3[(x^{2} +16)(x^{2} -16)]}{(x^{2} +16)}$

canceling  $(x^{2} +16)$ from numerator and denominator ,

$3(x^{2} -16)$  or

$3[(x)^{2} -(4)^{2} ]$

Again using formula but here the values of a and b are,

$a=x$  and  $b=4$

$3(x+4)(x-4)$

We get the answer of this question is $3(x+4)(x-4)$.