Formulas for abbreviated multiplication. Formula for the square of a binomial - $(a\pm b)^2=a^2\pm 2ab+b^2$
With this and the following lessons, we will try together to overcome the difficulties in solving various problems in which these formulas are applied. Let us recall them before we begin: 1. $(a \pm b)^{2}=a^{2}\pm 2ab+b^{2}$; 2. $(a-b)(a+b)=a^{2}-b^{2}$; 3. $(a \pm b)^{3}=a^{3}\pm 3a^{2}b+3ab^{2}\pm b^{3}$; 4. $(a \pm b)(a^{2}\pm ab+b^{2})=a^{3}\pm b^{3}$. In this article, we consider the formulas $(a\pm b)^{2}=a^{2}\pm 2ab+b^{2}$. Let's solve a few problems to show how we will apply them: Problem 1 Perform the grading $(2x+y)^{2}.$ Solution: Let's consider the formula $(a+b)^{2}=a^{2}+2ab+b^{2}$. In our expression, $2x$ plays the role of $a$ and $y$ plays the role of $b$. Let us now write $2x$ instead of $a$ and $y$ instead of $b$. Thus we get that $(2x+y)^{2}=(2x)^{2}+2.2x.y+y^{2}$. Now we need to exponentiate $(2x)^{2}$. Let's recall the following property learned in 6th grade $(a.b)^{n}=a^{n}.b^{n}$, hence $(2x)^{2}=2^{2}.x^{2}=4x^{2}$. Let us now, having made this c...