Find the Product:
\[ (1 – x)(1 + x + x^2) \]
Solution:
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=1,\qquad b=x \]
\[ (1 – x)(1 + x + x^2) \]
\[ = (1 – x)(1^2 + 1\cdot x + x^2) \]
\[ = 1^3 – x^3 \]
\[ = 1 – x^3 \]
\[ (1 – x)(1 + x + x^2) \]
Using identity:
\[ (a-b)(a^2+ab+b^2)=a^3-b^3 \]
Here, \[ a=1,\qquad b=x \]
\[ (1 – x)(1 + x + x^2) \]
\[ = (1 – x)(1^2 + 1\cdot x + x^2) \]
\[ = 1^3 – x^3 \]
\[ = 1 – x^3 \]