Question

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?

Answer 1

Answer:

a=16

Step-by-step explanation:

The distributive property states that

$a(b+c)=ab+ac$

Therefore using the distributive property

$(y - 4x)(y ^ 2 + 4y + 16)$

=$y(y ^ 2 + 4y + 16) - 4x(y ^ 2 + 4y + 16)$

Expanding the brackets

$y ^ 3 + 4y^2 + 16y - 4xy ^ 2 - 16xy - 64x$.....(i)

Comparing with the form

$y ^ 3 + 4y ^ 2 + ay - 4x y ^ 2 - axy - 64x$-----(ii)

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

Therefore, a=16