Use the identity (x+a)(x+b)=x2+(a+b)x+ab to find the following product.
(2a2+9)(2a2+5)
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Solution
Given: (2a2+9)(2a2+5) compare with (x+a)(x+b), we get x=2a2,a=9,b=5 Substitute the above values in given identity (x+a)(x+b)=x2+(a+b)x+ab ⇒(2a2+9)(2a2+5)=(2a2)2+(9+5)2a2+(9)(5) =4a4+14(2a2)+45 ∴(2a2+9)(2a2+5)=4a4+28a2+45