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Find the 4th term in the expansion of (5x + y)4 in simplest form.

Find the 4th term in the expansion of (5x + y)4 in simplest form.-example-1

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Answer:

= 625x^4 + 500x^3 y + 150x^2•y^2 + 20xy^3 + y^4

Explanation:

1. Use the Binomial Theorem.
( 5 x ) 4 + 4 ( 5 x ) 3 y + 6 ( 5 x ) 2 y 2 + 4 ( 5 x ) y 3 + y 4

STEPS

Apply the product rule to 5x.
5^4 x^4 + 4(5x)^3y + 6( 5x )^2y^2 + 4(5x)^y3 + y^4

Raise 5 to the power of 4.

625x^4 + 4(5x)^3y + 6(5x)^2y^2 + 4(5x)y^3 + y^4

Apply the product rule to 5x.

625^x^4 + 4( 5^3•x^3) y + 6(5x)^2y^2 + 4(5x)^y^3 + y^4

Raise 5 to the power of 3.

625x^4 + 4(125x^3) y + 6(5x)^2y^2 + 4(5x)y^3 + y^4

Multiply 125 by 4.

625x^4 + 500x^3•y + 6 ( 5 x )^2y^2 + 4(5x) y^3 + y^4

Apply the product rule to 5x.

625x^4 + 500x^3y + 6(5^2• x^2 )y^2 + 4(5x)y^3 + y^4

Raise 5 to the power of 2.

625 x 4 + 500 x 3 y + 6 ( 25 x 2 ) y 2 + 4 ( 5 x ) y 3 + y 4

Multiply 25 by 6.

625 x 4 + 500 x 3 y + 150 x 2 y 2 + 4 ( 5 x ) y 3 + y 4

Multiply 5 by4 .

625 x 4 + 500 x 3 y + 150 x 2 y 2 + 20 x y 3 + y 4



2. Simplify each term.
625x^4 + 500x^3 y + 150x^2•y^2 + 20xy^3 + y^4

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