Question

(x+5)(x+6)(x+7)....
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Answer 1

Answer:

Coefficient of x^2x

2

= 18

Coefficient of x = 107

Constant term = 210

Step-by-step explanation:

Given : Expression (x+5)(x+6)(x+7)(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)(x+5)(x+6)(x+7)

Using algebraic identity,

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

+(5+6)x+(5)(6)

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

2

+11x+30

The expression form,

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

2

+11x+30)(x+7)

Now writing coefficient as,

Coefficient of x^2x

2

, 7+11= 187+11=18

Coefficient of x, 77+30=10777+30=107

Constant term, 30\times 7=21030×7=210

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