Question

Complete the following product (x-3)(x^(2)+3x+9)

Answer 1

Given:

Given expression is equal to $(x-3)(x^2+3x+9)$.

To find:

We need to complete the product of given expression.

Solution:

In this question, we should find the product of given expression.

So, consider the given expression,

$\Rightarrow (x-3)(x^2+3x+9)$

Now, expand the terms present in the above expression.

$\Rightarrow x\times(x^2+3x+9)-3\times(x^2+3x+9)$

Multiplying the terms in the above expression,

$\Rightarrow x\times x^2+x\times3x+x\times9-3\times x^2-3\times3x-3\times9$

Simplifying the terms in the above expression,

$\Rightarrow x^3+3x^2+9x-3 x^2-9x-27$

Now write similar terms together.

$\Rightarrow x^3+3x^2-3 x^2+9x-9x-27$

$\Rightarrow x^3-27$

The above expression cannot be simplified further because there are no common terms.

Therefore, the product of given expression is equal to $x^3-27$.

Answer 2

SOLUTION

TO EVALUATE

$\sf{}(x - 3)( {x}^{2} + 3x + 9)$

EVALUATION

SOLVE USING ALGEBRAIC IDENTITY

We are aware of the identity that

$\sf{}(a - b)( {a}^{2} + ab + {b}^{2} ) = {a}^{3} - {b}^{3}$

Now

$\sf{}(x - 3)( {x}^{2} + 3x + 9)$

$= \sf{} {(x)}^{3} - {(3)}^{3} \: \: (using \: above \: identity)$

$\sf{} = {x}^{3} - 27$

SOLVE USING MULTIPLICATION

$\sf{}(x - 3)( {x}^{2} + 3x + 9)$

$= \sf{}x( {x}^{2} + 3x + 9) - 3( {x}^{2} + 3x + 9)$

$= \sf{} {x}^{3} + 3 {x}^{2} + 9x - 3 {x}^{2} - 9x - 27$

$\sf{} = {x}^{3} - 27$

━━━━━━━━━━━━━━━━

LEARN MORE FROM BRAINLY

If x+1/x=3 then, x^7+1/x^7=

https://brainly.in/question/23295932