Multiplying binomials

Multiply: $(x+2)(x+2)$

Test your result by plugging $x=3$ into both my original function, and your resultant function. Do they come out the same?

Multiply: $(x+3)(x+3)$

Test your result by plugging $x=-1$ into both my original function, and your resultant function. Do they come out the same?

Multiply: $(x+5)(x+5)$

Test your result by plugging $x=$ into both my original function, and your resultant function. Do they come out the same?

Multiply: $(x+a)(x+a)$

Now, leave $x$ as it is, but plug $a=3$ into both my original function, and your resultant function. Do you get two functions that are equal? Do they look familiar?

Do not answer these questions by multiplying them out explicitly. Instead, plug these numbers into the general formula for $(x+a{)}^2$ that you found in number 4.

• A

  $(x+4)(x+4)$

• B

  $(y+7{)}^2$

• C

  $(z+{)}^2$

• D

  $(m+\sqrt{2}{)}^2$

• E

  $(x-3{)}^2$ (*so in this case, $(a$ is –3.)

• F

  $(x-1{)}^2$

• G

  $(x-a{)}^2$

Earlier in class, we found the following generalization: $(x+a)(x-a)=x^2-a^2$ . Just to refresh your memory on how we found that, test this generalization for the following cases.

• A

  $x=\text{10}\text{,}a=0$

• B

  $x=\text{10}\text{,}a=1$

• C

  $x=\text{10}\text{,}a=2$

• D

  $x=\text{10}\text{,}a=3$

Test the same generalization by multiplying out $(x+a)(x-a)$ explicitly.

Now, use that “difference between two squares” generalization. As in #5, do not solve these by multiplying them out, but by plugging appropriate values into the generalization in #6.

• A

  $(\text{20}+1)(\text{20}-1)=$

• B

  $(x+3)(x-3)=$

• C

  $(x+\sqrt{2})(x-\sqrt{2})$

• D

  $(x+2/3)(x-2/3)$