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

$\sqrt{30}$ -------> 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)