Question

How do you find the product $(4{y^2} - 3)(4{y^2} + 7y + 2)$ ?

Answer 1

Hint: For solving this particular question , we have to simplify the expression by using algebraic identities and by performing arithmetic operations such as addition , subtraction , multiplication, and division . We have to convert numbers into its equivalent exponential form where required. Here we will use the distributive property as the basic step to solve the problem.

Complete step-by-step solution:
We have to simplify the given expression that is $(4{y^2} - 3)(4{y^2} + 7y + 2)$ ,
By applying Distribution Property that is $a(b + c) = ab + ac$we will get ,
$
  \Rightarrow (4{y^2} - 3)(4{y^2} + 7y + 2) \\
   \Rightarrow (4{y^2} - 3) \cdot 4{y^2} + (4{y^2} - 3) \cdot 7y + (4{y^2} - 3) \cdot 2 \\
 $
We can write this as,
\[ \Rightarrow 4{y^2} \cdot (4{y^2} - 3) + 7y \cdot (4{y^2} - 3) + 2 \cdot (4{y^2} - 3)\]
By applying Distribution Property that is $a(b + c) = ab + ac$we will get ,
$ \Rightarrow 16{y^4} - 12{y^2} + 28{y^3} - 21y + 8{y^2} - 6$
Now, combine like terms as ,
$ \Rightarrow 16{y^4} + 28{y^3} - 4{y^2} - 21y - 6$
Here, we get the required answer .

Hence the correct answer is $16{y^4} + 28{y^3} - 4{y^2} - 21y - 6$

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 .