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Question

How do you cube $$(x + 1)^{3} $$ ?

Solution
Verified by Toppr

One way to deal with it is to "break" it into chunks and use the "distributive" property, as:
$$(a + 1)^{3} = (x + 1) (x + 1) (x + 1) = $$
Let us the first $$2$$:
$$ = (x \cdot x + x \cdot 1 + 1 \cdot x + 1 \cdot 1 )(x + 1) = $$
$$ = (x^{2} + 2x + 1)(x + 1) = $$
now let us multiply the remaining $$2$$:
$$ = x^{2} \cdot x + x^{2} \cdot 1 + 2x \cdot x + 2x \cdot 1 + 1 \cdot x + 1 \cdot 1 = $$
$$ = x^{3} + x^{2} + 2x^{2} + 2x + x +1 = $$
$$ = x^{3} + 3x^{2} + 3x + 1 $$

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