Question

How do you expand $\left( {2x - 5} \right)\left( {x + 7} \right)$ ?

Answer 1

Hint: First in every problem try to recognize polynomials, identify binomials and trinomials.
Then find the product of a monomial and binomial.
A polynomial is the sum or difference of one or more monomials. If a polynomial has two terms it is called a binomial. If a polynomial has three terms it is called a trinomial.
After recognizing that find the product of two binomials and Use the distributive property to multiply any two polynomials
By this way we can easily expand any problems.

Complete step by step answer:
To expand the given solution, use the FOIL method which means a technique used for distributing two binomials.
The letters FOIL stand for First, Outer, Inner, Last. First means multiply the terms which
Occur first in each binomial, Outer means multiply the outermost terms in the product
Inner means multiply the innermost terms and last means multiply the terms which occur last in each binomial
$ \Rightarrow \left( {2x - 5} \right)\left( {x + 7} \right)$
Apply the distributive property
$ \Rightarrow \left( {2x - 5} \right)\left( {x + 7} \right)$
$ \Rightarrow 2x\left( {x + 7} \right) - 5\left( {x + 7} \right)$
Again use the same distributive property to expand the equation
\[ \Rightarrow 2x \times x + 2x \times 7 - 5 \times x - 5 \times 7\]
Now simplify and combine the terms,
$ \Rightarrow 2{x^2} + 14x - 5x - 35$
Now add $ + 14x$ and $ - 5x$ , we get
$ \Rightarrow 2{x^2} + 9x - 35$

Hence the expanded form of $\left( {2x - 5} \right)\left( {x + 7} \right)$ is $2{x^2} + 9x - 35$.

Note: "Expanding" means removing the () but we have to do it in the right way. () are called "parentheses" or "Brackets”. Whatever is inside the () needs to be treated as a "package"
So when we multiplying $ - $ multiply by everything inside the "package"
In case the given function has Power value, then the solving becomes tedious. In that case you can use the binomial theorem to expand a Function which makes the problem simpler.