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Fill in the missing coefficients in the expansion of the binomial (2x^2+y^2)^4

User Tomer Gal
by
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2 Answers

5 votes

Answer:

Given Expression
(2x^2+y^2)^4

To find: Expansion of expression

Consider,


(2x^2+y^2)^4\\\\\implies((2x^2+y^2)^2)^2

using identity,
(a+b)^2=a^2+b^2+2ab we get,


\implies((2x^2)^2+(y^2)^2+2*(2x^2)*(y^2))^2


\implies(4x^4+y^4+4x^2y^2)^2 (using law of exponent,
(x^a)^b=x^(ab) )

Now using identinty,
(x+y+z)^2=x^2+y^2+z^2+2xy+2yz+2xz we get,


\implies(4x^4)^2+(y^2)^2+(4x^2y^2)^2+2(4x^4)(y^2)+2(y^2)(4x^2y^2)+2(4x^2y^2)(4x^4)\\\\\implies16x^8+y^4+16x^4y^4+8x^4y^2+8x^2y^4+32x^8y^2

User Tomek G
by
8.2k points
2 votes
The expansion of the binomial:
( 2 x² + y² ) ^4 =

(2 x^(2) ) ^(4) + 4 * (2 x^(2) ) ^(3)* y^(2) + 6 * ( 2 x^(2) ) ^(2)*( y^(2)) ^(2) +4*2 x^(2) *( y^(2)) ^(3)+( y^(2)) ^(4)=

=16 x^(8)+32 x^(6) y^(2)+24 x^(4) y^(4) + 8 x^(2) y^(6)+ y^(8)
User PawanS
by
8.3k points

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