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Multiplication of a Binomial by a Trinomial

State whether...

Question

State whether True or False.
Multiply: $x^{2} + x + 1$ by $1 - x$ .
The answer is $1 - x^{3}$ .

A

True

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B

False

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Solution

The correct option is A True
$(x^{2} + x + 1) \times (1 - x)$
$= (x^{2} + x + 1) - x (x^{2} + x + 1)$
$= x^{2} + x + 1 - x^{3} - x^{2} - x$
$= 1 - x^{3}$

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