Question

উৎপাদকে বিশ্লেষণ কর: $(a^2-b^2)(x^2-y^2)+4abxy$

Answer 1

$(a^2-b^2)(x^2-y^2)+4abxy$

$=a^2(x^2-y^2)-b^2(x^2-y^2)+4abxy$

$=a^2x^2-a^2y^2-b^2x^2+b^2y^2$$+2abxy$$+2abxy$

$=a^2x^2+2abxy+b^2y^2-a^2y^2$$+2abxy$$-b^2x^2$

$=\{(ax)^2+2 \cdot ax \cdot by+ (by)^2\}$$-\{(ay)^2$$-2 \cdot ay \cdot bx $$+ (bx)^2\}$

$=(ax+by)^2-(ay-bx)^2$

$=\{(ax+by)+(ay-bx)\}$$\{(ax+by)-(ay-bx)\}$

$=(ax+by+ay-bx)(ax+by-ay+bx)$ [Answer]

Comments

Rules Applied:

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