Question

উৎপাদকে বিশ্লেষণ কর: $x^3+3x^2+3x+2$

Answer 1

$x^3+3x^2+3x+2$

$=x^3+3x^2+3x+1$$+1$

$=x^3+3\cdot x^2\cdot1+3\cdot x\cdot1^2$$+1^3$$+1$

$=(x+1)^3+1^3$

$=\{(x+1)+1\}\{(x+1)^2$$-(x+1)\cdot1$$+1^2\}$

$=(x+1+1)(x^2+2\cdot x\cdot1$$+1^2-x$$-1+1)$

$=(x+2)(x^2+2x+1-x$$-1+1)$

$=(x+2)(x^2+x+1)$ [Answer]

Comments

Rules Applied:

• $a^3+3a^2b+3ab^2+b^3=(a+b)^3$
• $a^3+b^3=(a+b)(a^2-ab+b^2)$
• $(a+b)^2=a^2+2ab+b^2$