iohanetc

2021-08-16

To calculate: The product of $[x-(3-i)][x-(3+i)]$

oppturf

Skilled2021-08-17Added 94 answers

Step 1

Polinomial identity:

1)$(a+b)(a-b)={a}^{2}-{b}^{2}$

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

Associative property,$(a+b)+c=a+(b+c)$

Step 2

If P(x) represents the give nexpression, then

$P\left(x\right)=[x-(3-i)][3-(3+i)]$

$P\left(x\right)=(x-3+i)(x-3-i)$

Use associative property of algebraic expressions,

Associative property is written as,

$(a+b)+c=a+(b+c)$

This property modifies the expressionas,

$P\left(x\right)=((x-3)+i)((x-3)-i)$

Apply arithmetic rule.

$(a+b)(a-b)={a}^{2}-{b}^{2}$

Here,

$a=(x-3),\text{}b=\left(i\right)$

Hence,

$P\left(x\right)={(x-3)}^{2}-{i}^{2}$

Apply arithmetic rule:

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

Here, NKS$a=x,\text{}b=3$

Since${\left(i\right)}^{2}=(-1)$ , the expression becomes,

$P\left(x\right)={(x-3)}^{2}-{i}^{2}$

$={x}^{2}-6x+9+1$

$={x}^{2}-6x+10$

Hence, the product of$[x-(3-i)][x-(3+i)]$ is ${x}^{2}-6x+10$

Polinomial identity:

1)

2)

Associative property,

Step 2

If P(x) represents the give nexpression, then

Use associative property of algebraic expressions,

Associative property is written as,

This property modifies the expressionas,

Apply arithmetic rule.

Here,

Hence,

Apply arithmetic rule:

Here, NKS

Since

Hence, the product of

Jeffrey Jordon

Expert2022-07-07Added 2605 answers

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