Question

How do you find the standard form of the following equation $Y = {(x + 3)^2} + 1$ ?

Answer 1

For solving this particular question, we have to use the identity that is ${(a + b)^2} = {a^2} + 2ab + {b^2}$ , then we have to simplify the expression by using algebraic identities and by performing arithmetic operations such as addition , subtraction , multiplication, and division .

Complete step by step solution:
We have given that ,
$Y = {(x + 3)^2} + 1$,
We have to find the standard form ,
Therefore, expand the given expression using the identity ${(a + b)^2} = {a^2} + 2ab + {b^2}$ ,
We will get the following ,
$Y = {x^2} + 2(x)(3) + {3^2} + 1$
Now try to make it less complex by combining like terms , do operations on like terms first in order to combine them then combine all the constant by doing so you will get you desired result ,
$Y = {x^2} + 6x + 9 + 1$
$= {x^2} + 6x + 10$
Here we get the required result.

Note: Before you evaluate an algebraic expression as given the question , your aim is to simplify it as much as possible . Simplifying an expression can make all of your calculations much easier and simpler. Here we are having some of the fundamental steps needed to simplify an algebraic expression: Step I. Always try to remove the parentheses given in the expression by multiplying with its corresponding factors. Step II. Simplify the given expression by using exponent rules to get rid of parentheses in terms of exponents. Step III. Try to make it less complex by combining like terms , do operations on like terms first in order to combine them. Step IV. Lastly, try to combine all the constants by doing so you will get your desired result .