Formula for the product of a sum by a difference of a binomial - $(a-b)(a+b)=a^2-b^2$
We continue with the next of the abbreviated multiplication formulas $(a-b)(a+b)=a^2-b^2$. Let's look at some problems to illustrate its applications. Problem 1 Perform the multiplication $(x+y)(x-y)$. Solution: Now we apply the formula $(a-b)(a+b)=a^2-b^2$, where $a=x$ and $b=y$, hence $(x-y)(x+y)=x^2-y^2$. Problem 2 Perform the multiplication $(3x-4y)(3x+4y)$. Solution: Apply the formula $(a-b)(a+b)=a^2-b^2$, where $a=3x$ and $b=4y$, hence $(3x-4y)(3x+4y)=(3x)^2-(4y)^2=9x^2-16y^2$. 3 Problem Perform the multiplication $(x^2-z)(x^2+z)$. Solution: Apply the formula $(a-b)(a+b)=a^2-b^2$, where $a=x^2$ and $b=z$, hence $(x^2-z)(x^2+z)=(x^2)^2-(z)^2=x^4-z^2$. Let us recall the power grading property, i.e. $(a^n)^m=a^{n.m}$. 4 Problem Calculate $17.23$ in a rational way. Solution: Represent the product $17.23$ in the following way $17.23=(20-3)(20+3)$ and apply the formula $(a-b)(a+b)=a^2-b^2$, so $17.23=(20-3)(20+3)=20^2-3^2=400-9=391$. 5 Problem Simplify the expression $(3x-...