Question

using algebraic identity find the coefficient of x square x cube x and constant term without actual expansion (X + 5)( x + 6)( X + 7)​

Answer 1

Step-by-step explanation:

Given expression is (X + 5)( x + 6)( X + 7)

This is in the form of the identity (x+a)(x+b)(x+c)

we know that

(x+a)(x+b)(x+c) =x^3+x^2(a+b+c)+(ab+bc+ca)x+abc

here a=5, b=6, c=7

then

(X + 5)( x + 6)( X + 7)=

=x^3+(5+6+7)x^2+(5×6+6×7+7×5)x+(5×6×7)

=x^3+18x^2+(30+42+35)x+(210)

=x^3+18x^2+107x+210

here x^3= x cube

and x^2 = x square

Answer 2

Answer:

Coefficient of x^2  = 18

Coefficient of x = 107

Constant term = 210

Step-by-step explanation:

Given: Expression  (x+5)(x+6)(x+7)

To find: Using algebraic identity find the coefficient of x Square x and constant term without actual expansion?

Solution :

Expression  (x+5)(x+6)(x+7)

Using algebraic identity,

(x+a)(x+b)=x^2+(a+b)x+ab

Here, a=5 and b=6

(x+5)(x+6)=x^2+(5+6)x+(5)(6)

(x+5)(x+6)=x^2+11x+30

The expression form,

(x+5)(x+6)(x+7)=(x^2+11x+30)(x+7)

Now writing coefficient as,

Coefficient of x^2, 7+11=18

Coefficient of x,  77+30+107

The  Constant term, 30*7

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