Question

What should be added to complete square of x4+64?

Answer 1

Answer:

16x^2

Step-by-step explanation:

x^4 + 64

(x^2 +8)^2

on expanding we get

x^4 + 16x^2 +32

hence 16 x^2 must be added

Answer 2

16x² should be added to complete square of x⁴ + 64

Given :

The expression x⁴ + 64

To find :

The expression should be added to complete square of x⁴ + 64

Formula Used :

$\displaystyle \sf {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is x⁴ + 64

Step 2 of 2 :

Find the required expression

$\displaystyle \sf {x}^{4} + 64$

$\displaystyle \sf = {( {x}^{2} )}^{2} + {(8)}^{2}$

$\displaystyle \sf = {( {x}^{2} )}^{2}+ {(8)}^{2} + 2. {x}^{2} .8 - 2. {x}^{2} .8$

$\displaystyle \sf = {( {x}^{2} + 8)}^{2} - 2. {x}^{2} .8\: \: \: \bigg[ \: \because \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \bigg]$

$\displaystyle \sf = {( {x}^{2} + 8)}^{2} - 16 {x}^{2}$

In order to get complete square we have to add 16x²

Hence 16x² should be added to complete square of x⁴ + 64

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ If a+b=7 and ab=4 and find Value of a² +b²

https://brainly.in/question/28413926

2. if (x+y) =9 and xy=6, find the value of x²+y²

https://brainly.in/question/23257499

#SPJ2