Question

How do you simplify $ {(x + 6)^2}? $

Answer 1

Hint: From the given above question, we have to find polynomials. So we use multiplication of a monomial by a polynomial and distributive property with exponent. First you multiply two terms together you must multiply the coefficient (numbers) and add the exponents. Next, distribute each term of the first polynomial to every term of the second polynomial. Finally, combine like terms (if you can).

Complete step-by-step solution:
Given,
 $ \Rightarrow {(x + 6)^2} $
First, we expand the square terms and we get
 $ \Rightarrow (x + 6)(x + 6) $
Then, we use reverse factorization in the above two polynomials.
So we get,
 $ \Rightarrow x(x + 6) + 6(x + 6) $
Next, we start with the first $ x $ and push it through to both $ x $ and 6 in the first polynomial.
We get,
 $ \Rightarrow {x^2} + 6x + 6(x + 6) $
Next, we start with the second part 6 and push it through to both $ x $ and 6 in the second polynomial. ,
We get,
 $ \Rightarrow {x^2} + 6x + 6x + 36 $
Now, we combine like terms and we get the required polynomial.
 $ \Rightarrow {x^2} + 12x + 36 $

$ {(x + 6)^2} $ is equal to $ {x^2} + 12x + 36 $ .

Note: There is another little hard way to find the answer.
First, expand the equation.
  $ \Rightarrow {(x + 6)^2} $
  $ \Rightarrow (x + 6)(x + 6) $
Next, we multiply (distribute) the first numbers of each set, outer numbers of each set, inner number of each set, and the last numbers of each set.
We get,
 $ \Rightarrow {x^2} + 6x + 6x + 36 $
Before step we use the FOIL (first, outer, inner, last) technique to distribute each expression.
Then combine like terms and we get,
 $ \Rightarrow {x^2} + 12x + 36 $
Therefore, we required polynomials.
In this question, students concentrate on multiplying each term of one polynomial by the other polynomial. And then, an exponent is a shorthand notation indicating how many times a number is multiplied by itself. When parentheses and exponents are involved, using the distributive property can make simplifying the expression much easier.
If you have three polynomials, you can multiply any two first, and then multiply this product by order. Sometimes you can’t combine the middle term.