Question

( a-4 b)^2-8 ab-17 b

Answer 1

${(a - 4b)}^{2} - 8ab - 17b = {a}^{2} - 8ab + {16b}^{2} - 8ab - 17b = {a}^{2} - 16ab + {16b}^{2} - 17b$

Answer 2

To simplify the expression, let's expand the square of the binomial first:

1. Expand (a - 4b)^2: (a - 4b)^2 = (a - 4b)(a - 4b) = a(a) + a(-4b) + (-4b)(a) + (-4b)(-4b) = a^2 - 4ab - 4ab + 16b^2 = a^2 - 8ab + 16b^2

Now, we can rewrite the original expression using the expanded form:

(a - 4b)^2 - 8ab - 17b = (a^2 - 8ab + 16b^2) - 8ab - 17b

Next, let's simplify it further by combining like terms:

(a^2 - 8ab + 16b^2) - 8ab - 17b = a^2 - 8ab + 16b^2 - 8ab - 17b

Now, combine the terms with 'ab' and 'b':

a^2 - (8ab + 8ab) + 16b^2 - 17b

2. Combine like terms: a^2 - 16ab + 16b^2 - 17b

So, the simplified expression is: a^2 - 16ab + 16b^2 - 17b