Show the terms and their factor by tree diagrams of the following algebraic expressions for $5x{y^2} + 7{x^2}y$.

Hint:Algebraic expressions are combinations of terms and mathematical operators. In the given algebraic expression the terms $5x{y^2}$ and $7{x^2}y$ are two different terms. These terms have different factors which we will show in the tree diagram.

Complete step by step answer:
Here, we are given the expression $5x{y^2} + 7{x^2}y$. We can split the expression in two terms as $5x{y^2}$ and $7{x^2}y$. Now, for the first term $5x{y^2}$ , we can write the factors of the term into numericals and variables as $5$ and $x{y^2}$. The factors of the variable term can be further written as $x$ and ${y^2}$. Similarly for the second term $7{x^2}y$ , we can write the factors as $7$ and ${x^2}y$. The factors of the variable term can be written as ${x^2}$ and $y$

The tree diagram can be drawn as follows:

This is how factors are represented in a factor tree . The factors for the given algebraic expressions are $5$ , $7$ , $x$ , $y$ , ${y^2}$ , ${x^2}$. A factor tree represents a factor which means that the terms in the algebraic expressions are divisible by factors we get at the end of the tree factor . We can also find H.C.F of a given algebraic expression by observing the co – efficiency of the given expression . For example , in the given question we have co – efficient $5$ and $7$. So, H.C.F of $5$ and $7$ is $1$ .

Note:We can find H.C.F using the prime factorization method , which you have learned in your previous classes. The factor tree provides information about factors so that the expression can be simplified. It also helps in cancelling out the additional expression so that the expression can be reduced.