Factoring Question?

Question

Factor completely:
3t^4x^2 - 48x^2

I left my notes at school..I have no idea even where to start on this one...Please help :)

Answer 1

You have one term:
3 t^4 x^2
and the other term is
48 x^2 = 3*16 x^2

Both terms have a 3 and x^2, so we'll factor that out.

(3x^2)(t^4) - (3x^2)(16)
(3x^2)(t^4 - 1)

now, note that t^4 - 1 is the difference of squares...

(3x^2)(t^2 - 1)(t^2 + 1)

and again, t^2 - 1 is the difference of squares...
(3x^2)(t - 1)(t + 1)(t^2 + 1)

done!

Answer 2

3t^4x^2 - 48x^2
=3x^2(t^4-16)
=3x^2(t^2+4)(t^2-4)
=3x^2(t^2+4)(t+2)(t-2)

Answer 3

Your notation is ambiguous. Is it
3t^(4x^2) - 48x^2

or 3t^(4x^2-48x^2) ?

The two equations are very different.

Answer 4

=3x^2 ( t^4 -16)
= 3x^2 ( t^2-4)(t^2+4)
= 3x^2 (t+2)(t-2) (t^2+4)
if you have done complex numbers you can further say
= 3x^2( t+2)(t-2)(t+2i)(t-2i)

Answer 5

Simplifying
3t4x2 + -48x2

Factor out the Greatest Common Factor (GCF), '3x2'.
3x2(t4 + -16)

Factor a difference between two squares.
3x2((t2 + 4)(t2 + -4))

Factor a difference between two squares.
3x2((t2 + 4)((t + 2)(t + -2)))Final result:3x2(t2 + 4)(t + 2)(t + -2)

Answer 6

3t^(4x² - 48x²)
= 3t^(-44x²)

Answer 7

3x^2(t^4-16)
3x^2(t^2-4)(t^2+4)
3x^2(t-2)(t+2)