Question

Using algebraic identities find the coefficients of $x^2$ term, $x$ term and constant term.

$(x+7)(x+3)(x+9)$

• A. $19,111,189$
• B. $19,-111,189$
• C. $19,111,-189$
• D. None of these

Answer 1

The correct option is A $19,111,189$

We solve the given expression $(x+7)(x+3)(x+9)$ as shown below:

$\left[\right(x+7\left)\right(x+3\left)\right](x+9)$

$=\left[x\right(x+3)+7(x+3\left)\right](x+9)$

$=(x^2+3x+7x+21)(x+9)$

$=(x^2+10x+21)(x+9)\left(Combiningliketerms\right)$

$=(x+9)(x^2+10x+21)$

$=x(x^2+10x+21)+9(x^2+10x+21)$

$=x^3+10x^2+21x+9x^2+90x+189$

$=x^3+(10+9)x^2+(21+90)x+189\left(Combiningliketerms\right)$

$=x^3+19x^2+111x+189$

From the above calculation, we observe that the coefficient of $x^2$ is $19$, the coefficient of $x$ is $111$ and the constant term is $189$.

Hence, the coefficient of $x^2$ is $19$, the coefficient of $x$ is $111$ and the constant term is $189$..