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Simple Expansions

Expanding Polynomial Factors

Here we apply some of the rules we have already learned to some brackets with more terms.

Example 4.

(x+a)^3=(x+a)*(x+a)^2=(x+a)*(x^2+2ax+a^2)=x*(x^2+2ax+a^2)+a*(x^2+2ax+a^2)=x(x^2)+x(2ax)+x(a^2)+a(x^2)+a(2ax)+a(a^2)=x^3+2ax^2+xa^2+2a^2*x+a^3=x^3+3ax^2+3a^2*x+a^3.

(x+y+z)^2=(x+y+z)*(x+y+z)=x(x+y+z)+y(x+y+z)+z(x+y+z)=x^2+xy+xz+yz+y^2+yx+zx+zy+z^2=x^2+y^2+z^2+2xy+2yz+2xz.

Exercise 4.

Expand the following expression. Be careful of notation and do not use spaces in your answer.

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