How do you simplify #5.6x^2 (y^2 - z^2) - 3.5y^2 (x^2 - z^2) + 2.7x^2 (y^2 - z^2) + 4.8y^2 (x^2 - z^2)#?

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Answer 1 · 2017-05-28T21:24:23

#8.3x^2(y^2-z^2)+1.3y^2(x^2-z^2)#

Strategy: Combine terms with identical expressions and factor like crazy.

Step 1. Combine terms with identical expressions.

#5.6color(red)(x^2(y^2-z^2))-3.5color(blue)(y^2(x^2-z^2))+2.7color(red)(x^2(y^2-z^2))+4.8color(blue)(y^2(x^2-z^2))#

#=5.6color(red)(x^2(y^2-z^2))+2.7color(red)(x^2(y^2-z^2))-3.5color(blue)(y^2(x^2-z^2))+4.8color(blue)(y^2(x^2-z^2))#

Step 2. Factor like crazy.

#=color(red)(x^2(y^2-z^2))(5.6+2.7)+color(blue)(y^2(x^2-z^2))(-3.5+4.8)#

#=color(red)(x^2(y^2-z^2))8.3+color(blue)(y^2(x^2-z^2))1.3#

#=8.3x^2(y^2-z^2)+1.3y^2(x^2-z^2)#