13. Use identities to find (a) (2x3 + 3y)(2x3 + 5y) (b) (y2 + 3/2)(y2 ? 3/2)
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(a)(2x3 + 3y)(2x3 + 5y)
Use identity
(x+a)(x+b)= x^2+(a+b)x+ab
Put x=2x^3,a=3y,b=5y
=( 2x^3)^2+(3y+5y)x+3y*5y
= 2x^5+8y+15y^2. Ans(a)
(b)(y2 + 3/2)(y2 - 3/2)
Use identity (x+a)(x-a)= x^2-a^2
Put x=y^2,b=3/2
== (Y^2)^2-(3/2)^2
== y^4-9/4. Ans(b)
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