an algebraic question from me.?

Do you mean Simplify?

Here..

4x(x-1)^(2)-16x

Squaring an expression is the same as multiplying the expression by itself 2 times.

(4x*(x-1)(x-1))-16x

Multiply each term in the first group by each term in the second group using the FOIL method. FOIL stands for First Outer Inner Last, and is a method of multiplying two binomials. First, multiply the first two terms in each binomial group. Next, multiply the outer terms in each group, followed by the inner terms. Finally, multiply the last two terms in each group.

(4x(x*x+x*-1-1*x-1*-1))-16x

Simplify the FOIL expression by multiplying and combining all like terms.

(4x(x^(2)-2x+1))-16x

Multiply 4x by each term inside the parentheses.

((4x^(3)-8x^(2)+4x))-16x

Remove the parentheses around the expression 4x^(3)-8x^(2)+4x.

(4x^(3)-8x^(2)+4x)-16x

Since 4x and -16x are like terms, add -16x to 4x to get -12x.

4x^(3)-8x^(2)-12x ANS....

or do you mean factor?

here's my answer like "tangy"

4x(x-1)^(2)-16x

Factor out the GCF of 4x from each term in the polynomial.

4x((x-1)^(2))+4x(-4)

Factor out the GCF of 4x from 4x(x-1)^(2)-16x.

4x((x-1)^(2)-4)

The binomial can be factored using the difference of squares formula, because both terms are perfect squares. The difference of squares formula is a^(2)-b^(2)=(a-b)(a+b).

4x((x-1)-2)((x-1)+2)

Remove the parentheses around the expression x-1.

4x(x-1-2)((x-1)+2)

Subtract 2 from -1 to get -3.

4x(x-3)((x-1)+2)

Remove the parentheses around the expression x-1.

4x(x-3)(x-1+2)

Add 2 to -1 to get 1.

4x(x-3)(x+1) ANS....

Do you mean factor?

4x(x-1)^2-16x

Common factor is 4x. Factor it out.

4x [ (x-1)^2 - 4 ]

The expression inside the [ ] in the previous line is a difference of two squares.

4x [(x-1)-2] [(x-1)+2]

Simplify each of the term inside the [ ] in the previous line.

4x(x-3)(x+1)