Question

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

Answer 1

Answer:

x^2 coefficient is 18

x coefficient is 107

constant term is 210

Step-by-step explanation:

if we see this identity ...it's seems like a cubic equation solution ..that's root -5,-6,-7. ....then the coefficient of x^2 is sum of roots and coefficient of x is (-5×-6+-6×-7+-5×-7). and constant term is product of roots

Answer 2

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

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

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

The expression form,

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

Now writing coefficient as,

Coefficient of $x^2$ ,   $7+11= 18$

Coefficient of x,  $77+30=107$

Constant term,  $30\times 7=210$

#Learn more

Using algebraic identily find the coefficients of x² and x

and constant team with out actual expression

i) (2x + 3) (2x - 5)(2x-6)

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