How do you find the product of #(-y-3x)(-y+3x)#?

1 Answer
smendyka
Feb 26, 2017

See the entire solution process below:

Explanation:

Solution 1) We can use this formula:

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

Substituting #-y# for #a# and #3x# for #b# gives:

#(-y + 3x)(-y - 3x) = (-y)^2 - (3x)^2 = y^2 - 9x^2#

Solution 2) To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.

#(color(red)(-y) - color(red)(3x))(color(blue)(-y) + color(blue)(3x))# becomes:

#(color(red)(-y) xx color(blue)(-y)) + (color(red)(-y) xx color(blue)(3x)) - (color(red)(3x) xx color(blue)(-y)) - (color(red)(3x) xx color(blue)(3x))#

#(-y)^2 - 3xy + 3xy - 9x^2#

We can now combine like terms:

#y^2 + (-3 + 3)xy - 9x^2#

#y^2 + 0xy - 9x^2#

#y^2 - 9x^2#

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