Expand and Simplify?

Question

how would I do..

(2a -1)(2a +1) - (a -3)(a + 3)

and,

(-2t - r)(-3 + r)

thanks.

Answer 1

(2a-1)(2a+1) - (a-3)(a+3)

=(4a^2 + 2a - 2a - 1) - (a^2 + 3a - 3a -9)
=(4a^2 - 1) - (a^2 -9)
=(3a^2 +8) ANSWER

(-2t - r)(-3 + r)
= ( 6t - 2tr + 3r - r^2 )
= 3( 2t + r ) -r ( 2t + r )
= ( 2t + r ) ( 3 - r ) ANSWER

Answer 2

Take time to learn the three rules for this sort of multiplication. You will NEED to know it next week or next semester, and it is as neat as it is handy.

(2a-1)(2a+1) and (a -3)(a + 3) both follow the conjugate rule :
(x-y)(x+y)=
x^2 + xy - yx - y^2 = ( "x^2" is the notation for "x squared")
x^2 - y^2
so:
(2a-1)(2a+1) =
(2a)^2 - (1)^2 =
4*(a^2) - 1
and:
(a -3)(a + 3) =
a^2 - 3^2 =
a^2 - 9

This is what is ment with expanding.
You are now left with the following expression:
( 4*(a^2) - 1 ) - ( a^2 - 9 )
wich is solved by the following operations:

(4 - 1)*(a^2) + (-1 - (-9)) , where the double minus equals a pluss.

And at last you get:

3 a^2 + 8
Wich is nice and simplified...
I hope that helped for more than just that one homework asignment.

Answer 3

use FOIL (multiply First terms, Outer terms, Inner terms and Last terms)

2a(2a)+2a(1)-1(2a)-1(1)-[a(a)+a(3)-3(a)-3(3)]
=4a^2+2a-2a-1-(a^2+3a-3a-9) combine like terms 2a and -2a, 3a &-3a to get
=4a^2-1-(a^2-9) distribute the -1 in front of a^2-9 to get
=4a^2-1-a^2+9 combine like terms 4a^2 & -a^2 and -1& 9 to get
=3a^2+8

the second one
-2t(-3)-2t(r)+r(3)-r(r)
=6t-2rt+3r-r^2

Answer 4

(2a-1)(2a+1)-(a-3)(a+3)

2 2 2
(4 a + 2a-2a- 1)-(a +3a-3a-9)
2 2
4a -1 - a +9
2
3a +8
Answer

(-2t-r)(-3t+r)

2 2
6t -2tr+3tr -r

2 2
6t +tr -r

Answer

Answer 5

(2a - 1)(2a + 1) - (a - 3)(a + 3)
= 4a^2 - 1 - a^2 - 9
= 3a^2 - 10

and

6t -2rt + 3r - r^2

Answer 6

1) (4a^2 -1) - (a^2 - 9) = 3a^2 + 8

2) (6t -2tr + 3r +r^2)