Question

উৎপাদকে বিশ্লেষণ কর: $8x^3+12x^2+6x-63$

Answer 1

$8x^3+12x^2+6x-63$

$=8x^3+12x^2+6x$$+1-64$

$=\left(2x\right)^3+3\cdot\left(2x\right)^2\cdot1$$+3\cdot2x\cdot\left(1\right)^2$$+\left(1\right)^3$$-64$

$=\left(2x+1\right)^3-\left(4\right)^3$

$=\left\lbrace\left(2x+1\right)-4\right\rbrace$$\{\left(2x+1\right)^2$$+\left(2x+1\right)\cdot4$$+4^2\}$

$=\left(2x+1-4\right)$$\{\left(2x\right)^2$$+2\cdot2x\cdot1$$+1^2+8x$$+4+16\}$

$=(2x-3)(4x^2+4x+1+8x$$+4+16)$

$=(2x-3)(4x^2+12x$$+21)$ [Answer]

Comments

Rules Applied:

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