How do you find the product #(2+x)(2-x)#?

2 Answers
Apr 16, 2017

Answer:

See the entire solution process below:

Explanation:

This is a special case described by:

#(a + b)(a - b) = a^2 - b^2#

Letting #a# equal #2# and #b# equal #x# and substituting gives:

#(2 + x)(2 - x) = 2^2 - x^2 = 4 - x^2#

We can also multiply the two terms using this process. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(2) + color(red)(x))(color(blue)(2) - color(blue)(x))# becomes:

#(color(red)(2) xx color(blue)(2)) - (color(red)(2) xx color(blue)(x)) + (color(red)(x) xx color(blue)(2)) - (color(red)(x) xx color(blue)(x))#

#4 - 2x + 2x - x^2#

We can now combine like terms:

#4 + (-2 + 2)x - x^2#

#4 + 0 - x^2#

#4 - x^2#

Apr 16, 2017

Answer:

Use the distributive property and then combine common terms.
# ( 4 - x^2)#

Explanation:

Use the distributive property to multiply the parenthesis. This gives.

# (2 + x) xx ( 2-x) = 2 xx (2 -x) + x xx ( 2-x) # Multiplying across gives

# 2 xx ( 2 -x ) + x xx (2-x) = 4 - 2x + 2x - x^2# Combining like terms

# 4 - x^2#