Question
Find the following products: $(1 + x)(1 - x + x^2)$
✓
Answer
We have,
$(1 + x)(1 - x + x^2)$
$= (1 + x)\big[(1)^2 - 1 \times x + (x)^2\big]$
$= 1^3 + x^3 \big[\because a^3 - b^3 = (a + b)(a^2 - ab + b^2)\big]$
$\therefore (1 + x)(1 -+ x + x^2) $
$= 1 + x^3$
$(1 + x)(1 - x + x^2)$
$= (1 + x)\big[(1)^2 - 1 \times x + (x)^2\big]$
$= 1^3 + x^3 \big[\because a^3 - b^3 = (a + b)(a^2 - ab + b^2)\big]$
$\therefore (1 + x)(1 -+ x + x^2) $
$= 1 + x^3$
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