Essay, show all work. find the following product. (y-8)^2
(y-8)(y-8)
using distributive property of multiplication:
y(y-8) - 8(y-8)
y^2 - 8y -8y + 64
y^2 - 16 y + 64
(a-b)^2 = a^2 - 2ab + b^2
(y-8)^2 = y^2 - 2*y*8 + 8^2
(y-8)^2 = y^2 - 16y + 64
To find the product of (y-8)^2, we need to use the concept of expanding binomial squares.
To expand a binomial square, we can use the formula (a-b)^2 = a^2 - 2ab + b^2.
In this case, our binomial is (y-8), so we will substitute 'a' with 'y' and 'b' with '8' in the formula and apply the exponent of 2:
(y-8)^2 = y^2 - 2(y)(8) + 8^2
Simplifying this expression further, we get:
(y-8)^2 = y^2 - 16y + 64
Therefore, the product of (y-8)^2 is y^2 - 16y + 64.
Remember, when expanding binomial squares, it's essential to apply the exponent to both terms within the parentheses and then simplify the resulting expression.