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Using the distributive property to find the product (y - 4x)(y ^ 2 + 4y + 16) results in a polynomial of the form y ^ 3 + 4y ^ 2 + ay - 4x * y ^ 2 - axy - 64x . What is the value of a in the polynomial?

Respuesta :

Answer:

a=16

Step-by-step explanation:

The distributive property states that

[tex]a(b+c)=ab+ac[/tex]

Therefore using the distributive property

[tex](y - 4x)(y ^ 2 + 4y + 16)[/tex]

=[tex]y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)[/tex]

Expanding the brackets

[tex]y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x[/tex].....(i)

Comparing with the form

[tex]y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x[/tex]-----(ii)

The coefficient of y in (i) is 16 which corresponds to a and the likewise the coefficient of xy

Therefore, a=16

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