Question

Find the two products below. Compare and contrast, in complete sentences, the similarities and differences of the two.

(x + 4)(x − 4) and (x + 4)(x + 4)

Answer 1

What do you get when you multiply out (x + 4)(x − 4)

Answer 2

x^2-16?

Answer 3

and what about (x + 4)(x + 4)

Answer 4

x^2+8x+16

Answer 5

good, you are correct on both

Answer 6

so what do x^2-16 and x^2+8x+16 have in common

Answer 7

16

Answer 8

and?

Answer 9

x^2

Answer 10

good

Answer 11

so both are quadratic expressions

Answer 12

or polynomials of degree 2

Answer 13

now onto the differences

Answer 14

8x

Answer 15

good, the second expression has that middle term 8x

Answer 16

so the second expression has 3 terms while the first has 2 terms

Answer 17

the first is a difference of squares

the second is a perfect square

Answer 18

Another difference:

the first is a binomial

the second is a trinomial

Answer 19

thank you!

Answer 20

oh another similarity is that both are special products...basically they have specific formulas for these cases

formulas are:

(a-b)(a+b) = a^2 - b^2 ... Difference of squares

(a+b)(a+b) = a^2 + 2ab + b^2 ... Perfect Square Trinomial

Answer 21

you're welcome