Question

which of the following is not a difference of two square?

a.1/4x⁴-1
b.x²-0.0001y⁴
c.16(x-1)²-49
d.(x+1)4-4x6​

Answer 1

a and b

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Answer 2

Given:

The options

• $\dfrac{1}{4x^{4}-1}$

• $x^{2}-0.0001y^{4}$

• $16(x-1)^{2}-49$

• $(x+1)^{4}-4x^{6}$

To find:

Which of the above is not a difference of two squares

Step-by-step explanation:

a. $\dfrac{1}{4x^{4}-1}$

$=\dfrac{1}{(2x^{2})^{2}-(1)^{2}}$

This shows that option a is not a square difference.

b. $x^{2}-0.0001y^{4}$

$=(x)^{2}-(0.01y^{2})^{2}$

This shows that option b is a square difference.

c. $16(x-1)^{2}-49$

$=\{4(x-1)\}^{2}-7^{2}$

This shows that option c is a square difference.

d. $(x+1)^{4}-4x^{6}$

$=\{(x+1)^{2}\}^{2}-(2x^{3})^{2}$

This shows that option d is a square difference.

Final Answer:

Option a $\dfrac{1}{4x^{4}-1}$ is not a square difference.