Question

Is this a difference of squares? x2−30

1. Yes because it involves a minus sign

2. Yes because it starts with an x2

3. No because it starts with an x2

4. No because the 30 is not a perfect square number

Factor this difference of squares.
16x2−25

1. (16x−5)(16x+5)

2. (4x−5)(4x+5)

3. (4x−25)(4x+25)

4. (4x2−5)(4x2+5)

Answer 1

we know that

The difference of squares is two terms that are squared and separated by a subtraction sign

so

`a^(2)-b^(2)=(a+b)*(a-b)`

Part a)

we have

`x^(2)-30`

we know that

`√(30)` -------> is not a integer

so

The number 30 is not a perfect square number

therefore

the answer part a) is the option

4. No because the 30 is not a perfect square number

Part b)

we have

`(16x^(2)-25)`

we know that

`16x^(2)=(4x)^(2) \\25=5^(2)`

so

`(16x^(2)-25)=(4x)^(2)-5^(2)=(4x+5)*(4x-5)`

therefore

the answer part b) is the option

2. (4x−5)(4x+5)