find the co efficent of x3in the expense of 1+4x|3 whole raise power 7
Answers
Answer: Please mark me as brainliest
For example, I have done like this
Step-by-step explanation:
the Coefficient of x in the expansion of ( x + 3 )^3 is 27.
Step-by-step-explanation:
It is said to find the coefficient of x in expansion ( x + 3 )^3, so first of all we have to expand the equation by using ( a + b )^3 = a^3 + b^3 + 3ab( a + b ).
Applying this formula by assuming an as x and b as 3.
Thus,
= > ( x + 3 )^3
= > ( x )^3 + ( 3 )^3 + 3( x × 3 )( x + 3 )
= > x^3 + 27 + 3( 3x )( x + 3 )
= > x^3 + 27 + 9x( x + 3 )
= > x^3 + 27 + 9x^2 + 27x
Now, we have expanded the equation, and now it is x^3 + 27 + 9x^2 + 27x.
According to the question, we have to find out the coefficient of x and in the expanded equation, the coefficient of x is 27, as it is the term present in product form with x.
Thus,
Coefficient of x in the expansion of ( x + 3 )^3 is 27.
Or
The question revolves around the formulae of Identity:
(a+b)³
If we know the expansion of this formula (a+b)³, then we can easily solve this question.
The change is just that 'a' is given as 'x' so the identity becomes : (x+3)³
The question is all about just finding the coefficient of 'x'.
But first of all, before finding the coefficient we need to expand the identity (x+3)³ using suitable assumptions
So, the expansion of (a+b)³ is:
a³ + b³ + 3ab (a + b)
We will use this formula to find the coefficient of 'x' but the identity is changed a bit so we need to make some suitable substitution for the same.
So, assume 'a' as 'x' and assume 'b' as '3'.
The equation (identity)then becomes, (x+3)³ instead of (a+b)³
(x+3)³ = x³ + 3³ + 3 (x × 3) (x + 3)
= x³+27+3 (3x) (x+3)
= x³+27 + 9x (x+3)
= x³+27+ 9x²+ 27x
Now, the identity (x+3)³ is in the simplest form
We have two coefficient along with 'x' variables, 9 and 27.
But according to the question:
We need to find the coefficient of 'x' variables which is 27.
But why not 9 can be the coefficient of x?
9 can't be coefficient of x because it has x in the form of x², but the question is about to find the coefficient of x and not of x², so 27 is the coefficient of x.
We satisfied the condition needed in the question:
1. To find the coefficient of x in the expanded form.
The coefficient of x = 27.