Question

Fill in the empty spaces with monomials that make each equality into an indentity.

(4 - ...)^2 = 16-8a + ...

and

(3x − ...)^2 = 9x^2−6x+1

Answer 1

First one:

(4-a)^2=16-8a+a^2

Second:

(3x-1)^2=9x^2-6x+1

Answer 2

9514 1404 393

Answer:

• a, a²
• 1

Explanation:

The form you're trying to match is ...

(p +q)^2 = p^2 +2pq +q^2

__

a) We can see that p = 4 and ...

2pq = -8a

2·4·q = -8a . . . . . use the known value of p

q = -a . . . . . . . . . divide by 8

So, the identity is ...

(4 -a)^2 = 16 -8a +a^2

__

b) We see that p=3x, 2pq = -6x, and q^2 = 1. As above, we conclude ...

2(3x)q = -6x

q = -1 . . . . . consistent with q^2 = 1

The identity is ...

(3x -1)^2 = 9x^2 -6x +1