Formulas for abbreviated multiplication. Formula for the cube of a binomial - $(a\pm b)^3=a^3\pm 3a^2b+3ab^2\pm b^3$
We continue with the next of the abbreviated multiplication formulas $(a\pm b)^3=a^3\pm 3a^2b+3ab^2\pm b^3$. Let's look at some problems to illustrate some of its applications. Problem 1 Perform the grading $(x+2)^3$. Solution: To solve this problem we will apply the formula $(a+b)^3=a^3+3a^2b+3ab^2+b^3$, where in our case $a=x$ and $b=2$, so we get $(x+2)^3=x^3+3x^2.2+3x.2^2+2^3=x^3+6x^2+12x+8$. Problem 2 Perform the $(2m-3n)^3$ grading. Solution: $(2m)^2.3n+3.(2m).(3n)^2-(3n)^3=8m^3-36m^2n+54mn^2-27n^3.$ 3 Problem Perform the grading $(3t+z^2)^3$ Solution: To solve this problem we will apply the formula $(a+b)^3=a^3+3a^2b+3ab^2+b^3$, where $a=3t$ and $b=z^2$, hence $(3t+z^2)^3=(3t)^3+3. (3t)^2.z^2+3.(3t)(z^2)^2+(z^2)^3=27t^3+27t^2z^2+9z^4t+z^6.$ 4 Problem Simplify the expression $(x+1)^3-2(x-1)^2.$ Solution: Notice that the expression we need to simplify involves two of the shortcut multiplication formulas $(a+b)^3=a^3+3a^2b+3ab^2+b^3$ and $(a-b)^2=a^2-2ab+b^2$, the latter...