To calculate: The product of [x−(1+2)][x−(1−2)].

Question

wornoutwomanC · Accepted Answer

Step 1
Given:
Algebraic expression in multiplication form, $[x - (1 + \sqrt{2})] [x - (1 - \sqrt{2})]$
Formula Used:
Polynomial identity,
$(a - b) (a + b) = a^{2} - b^{2}$
$(a - b)^{2} = a^{2} 2 a b + b^{2}$
Associative property, $(a + b) + c = a + (b + c)$
Step 2
If $P (x)$ represent the given expression, then
$P (x) = [x - (1 + \sqrt{2})] [x - (1 - \sqrt{2})]$
$P (x) = (x - 1 - \sqrt{2}) (x - 1 + \sqrt{2})$
Use associative property of algebraic expressions.
Associative property is written as.
$(a + b) + c = a + (b + c)$
This property modifies the expression as,
$P (x) = ((x - 1) - \sqrt{2}) ((x - 1) + \sqrt{2})$
Apply arithmetic rule.
$(a - b) (a + b) = a^{2} - b^{2}$
Here, $a = (x - 1), b = (\sqrt{2})$
Hence,
$P (x) = {(x - 1)}^{2} - ({\sqrt{2}}^{2}$
Apply arithmetic rule:
${(a - b)}^{2} = a^{2} - 2 a b + b^{2}$
Here, $a = x, b = 1$
Hence,
$P (x) = x^{2} - 2 x + 1 - 2$
$= x^{2} - 2 x - 1$
Hence, the product of $[x - (1 + \sqrt{2})] [x - (1 - \sqrt{2})]$ is $x^{2} - 2 x - 1 .$

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

To calculate: The product of [x-(1+\sqrt{2})][x-(1-\sqrt{2})].

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