गुणनखण्ड कीजिए : (a) `x^(4)+4x^(2)+16` (b) `x^(4)+4` 
गुणनखण्ड कीजिए : (a) `x^(4)+4x^(2)+16` (b) `x^(4)+4` 




solution: (a) यहाँ `x^(4)+4x^(2)+16=(x^(2))^(2)+2(x^(2))(4)+(4)^(2)-8x^(2)+4x^(2)` <br> `" "` [हम सूत्र `a6(2)+2ab+b^(2)=(a+b)^(2)` बनाने का प्रयास कर रहे है] <br> `=(x^(2)+4)^(2)-4x^(2)=(x^(2)+4)^(2)-(2x)^(2)` <br> `=(x^(2)+4+2x)(x^(2)+4-2x)" "[becausea^(2)-b^(2)=(a+b)(a-b)]` <br> `=(x^(2)+2x+4)(x^(2)-2x+4)` <br> (b) `x^(4)+4=(x^(2))^(2)+(2)^(2)` <br> `underbrace((x^(2))^(2)+2(x^(2))(2)+(2)^(2))-2(x^(2))(2)" "` (समान राशि जोड़ने और घटाने पर) <br> `=(x^(2)+2)^(2)-4x^(2)` <br> `=(x^(2)+2)^(2)-(2x)^(2)=(x^(2)+2+2x)(x^(2)+2-2x)=(x^(2)+2x+2)(x^(2)-2x+2)` 
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