Question 67365
the answers will be in red<br>

1)Find each of the following squares.
(7p+6q)^2<br>

(7p+6q)^2=(7p+6q)(7p+6q)<br>

now just use the foil method<br>

f = 7p(7p)
o = 7p(6q)
i = 7p(6q)
l = 6q(6q)<br>

(7p+6q)(7p+6q)
=7p(7p)+7p(6q)+7p(6q)+6q(6q)
=49p^2+42pq+42pq+36q^2
<font color = red>=9p^2-84pq+36q</font><br>

2)Find each of the following squares.
(w minus(1)divided by (4))^2<br>

(w minus(1)divided by (4))^2 = (w-1)^2/4^2<br>

(w-1)^2 = (w-1)(w-1)<br>

we use foil again on the top<br>

f = w(w)
o = w(-1)
i = -1(w)
l = -1(-1)<br>

(w-1)(w-1)
= w(w)+w(-1)+-1(w)+-1(-1)
=w^2-w-w+1
=w^2-2w+1<br>

(w-1)^2/4^2
<font color = red>=(w^2-2w+1)/16</font><br>

3)Find each of the following products.
a(a+5)(a-5)<br>

use foil first<br>

f = a(a)
o = a(-5)
i = 5(a)
l = 5(-5)<br>

(a+5)(a-5)
= a(a)+a(-5)+5(a)+5(-5)
= a^2-5a+5a-25
=a^2-25

now distribute

a(a+5)(a-5)
=a(a^2-25)
<font color = red>=a^3-25a</font>