Question

উৎপাদকে বিশ্লেষণ কর: $2b^2c^2+2c^2a^2+2a^2b^2$$-a^4-b^4-c^4$

Answer 1

$2b^2c^2+2c^2a^2+2a^2b^2$$-a^4$$-b^4$$-c^4$

$=4a^2b^2$$-a^4-b^4-c^4-2a^2b^2$$+2b^2c^2$$+2c^2a^2$

$=4a^2b^2$$-(a^4+b^4+c^4$$+2a^2b^2-2b^2c^2$$-2c^2a^2)$

$=4a^2b^2$$-\{(a^2)^2+(b^2)^2+(-c^2)^2$$+2a^2b^2+2b^2(-c^2)$$+2(-c^2)a^2\}$

$=4a^2b^2$$-\{ a^2+b^2+(-c^2)\}^2$

$=(2ab)^2-(a^2+b^2-c^2)^2$

$=\{2ab+(a^2+b^2-c^2)\}$$\{2ab-(a^2+b^2-c^2)\}$

$=(2ab+a^2+b^2-c^2)$$(2ab-a^2-b^2+c^2)$

$=\{(a^2+2ab+b^2)-c^2\}$$\{c^2-(a^2-2ab+b^2)\}$

$=\{(a+b)^2-c^2\}$$\{c^2-(a-b)^2\}$

$=\{(a+b)+c\}\{(a+b)-c\}$$\{c+(a-b)\}\{c-(a-b)\}$

$=(a+b+c)(a+b-c)$$(c+a-b)(c-a+b)$

$=(a+b+c)(a+c-a)$$(a-b+c)(a+b-c)$ [Answer]

Comments

Rules Applied:

• $a^2+b^2+c^2+2ab+2bc+2ca=(a+b+c)^2$
• $a^2-b^2=(a+b)(a-b)$
• $a^2+2ab+b^2=(a+b)^2$
• $a^2-2ab+b^2=(a-b)^2$