How do you simplify #7xy (x^2 + y) - 11 xy^2 (x^2 -1)#?

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Answer 1 · 2015-04-25T07:08:01

#7xy (x^2 + y) - 11 xy^2 (x^2 -1)#

We know that #color(blue)(a*(b+-c) = a*b +-a*c#

# = 7xy*x^2 + 7xy*y -11xy^2*x^2 - 11xy^2#

# = 7(x*x^2)*y + 7x(y*y) - 11(x*x^2)(y^2) - 11xy^2#

We also know that #color(blue)(a^m * a^n = a^(m+n)#

# = 7(x^(2+1))*y + 7x(y^(1+1)) - 11(x^(2+1))(y^2) - 11xy^2#

# = 7x^3y + 7xy^2 - 11x^3y^2 - 11xy^2#

# = 7x^3y + (7xy^2 - 11xy^2) - 11x^3y^2#

# = 7x^3y - 4xy^2 - 11x^3y^2#

# =color(green)( - 11x^3y^2 + 7x^3y - 4xy^2 #