The Algebraic Expression "A2B2+2Ab": Explanation And Solution

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Introduction

Algebra is a branch of mathematics that deals with symbols and the rules for manipulating these symbols. In algebra, we use letters to represent unknown numbers and symbols to represent operations. One of the most common algebraic expressions is "a2b2+2ab". In this article, we will explain what this expression means and how to solve it.

Understanding the Expression

The expression "a2b2+2ab" contains two terms: "a2b2" and "2ab". The term "a2b2" means "a squared times b squared", while the term "2ab" means "two times a times b". To understand this expression better, let's use some values for a and b. For example, if a=3 and b=4, then "a2b2+2ab" becomes "324+24", which equals 348.

Simplifying the Expression

To simplify the expression "a2b2+2ab", we need to factor it. Factoring means finding the common factors of the terms in the expression. In this case, the common factor is "ab". We can factor out "ab" to get "ab(a+b)". Therefore, "a2b2+2ab" equals "ab(a+b)".

Using the Expression in Real Life

The expression "a2b2+2ab" can be used in real-life situations, such as calculating the area of a rectangle. If we have a rectangle with sides "a" and "b", the area can be calculated using the formula "a times b". However, if we want to calculate the area of a rectangle with sides "a+1" and "b+1", we can use the expression "a2b2+2ab" to simplify the calculation. The expression becomes "(a+1)2(b+1)2+2(a+1)(b+1)", which can be simplified to "ab+2a+2b+2".

Using the Expression in Algebraic Equations

The expression "a2b2+2ab" can also be used in algebraic equations. For example, if we have the equation "a2b2+2ab-6=0", we can use the expression to solve for "a" and "b". We can factor the expression to get "(ab+3)(ab-2)=0". Therefore, "ab+3=0" or "ab-2=0". Solving for "a" and "b" gives us the solutions "a=-3/b" or "a=2/b".

Conclusion

In conclusion, the algebraic expression "a2b2+2ab" can be used in various situations, such as calculating the area of a rectangle or solving algebraic equations. To simplify the expression, we need to factor it by finding the common factors of the terms. By understanding this expression, we can apply it to real-life situations and solve complex algebraic equations.