can you help me with some algebra?

Question

factor completely:

1. 9a^2 - 100

2. 2a^4 - 18a^2

3. t^2 -(t - 1)^2

Answer 1

PROBLEM 1:

Difference of squares:
(3a)² - 10²

= (3a + 10)(3a - 10)

PROBLEM 2:

Factor out a 2a²:
2a²(a² - 9)

Now you have a difference of squares again:
2a²(a + 3)(a - 3)

PROBLEM 3:

t² - (t - 1)²

Difference of squares again
(t + (t-1))(t - (t-1))

Simplify:
(2t - 1)(+1)

Get rid of the extraneous +1 multiplier:
2t - 1

(You could also get there by expanding the prior expression with FOIL).

Answer 2

sure, first know what difference of squares means, okay?!
(a² - b²) = (a - b)(a + b)

1. 9 and 100 are perfect squares of 3 and 10, respectively
that is, 3² = 9 and 10² = 100
a² of course is a square of a
(3a - 10)(3a + 10)

2. take the common factors out of both terms
2a² is a factor of both terms,okay
2a²(a² - 9) = 2a²(a - 3)(a + 3)

3. t² - (t - 1)² carry out the mulitplication first here using foil method on the second term
t² - (t -1)(t -1) =
t² - (t² - 2t + 1) =
2t - 1

Answer 3

One must have an equation
[9a^2 - 100 is not an equation]
1. 9a^2 - 100=0 is an equation
then
a= + - sqrt( 100/9) = + - 10/3
the roots are a1=10/3 ; a2=-10/3 finally
9a^2 - 100=(a-10/3)(a+10/3)

2. 2a^4 - 18a^2=0
2a^2 - 18=0
a= + - sqrt( 18/2) = + - 3
a1=3 a2=-3
2a^2 - 18=(a+3)(a-3)

3. t^2 -(t - 1)^2= 0

t^2 -t^2 +2t - 1= 0
2t=1
t= 1/2

Answer 4

(3a-10)(3a+10)

2a^2(a^2-9)=2a^2(a-3)(a+3)

t ^2-(t-1)^2
t^2(-t+1)^2
t^2-t^2+2t+1=2t-1
2t-1=0
t=1/2