Solve (a-4)(a-4): Expanding a Repeated Binomial Expression

Question

(a4)(a4)=? (a-4)(a-4)=\text{?}

Video Solution

Solution Steps

00:00 Solve
00:03 A factor multiplied by itself is actually a square
00:08 Let's use this formula and square the parentheses
00:18 Let's use the shortened multiplication formulas to expand the parentheses
00:35 Let's calculate the multiplication
00:38 And this is the solution to the question

Step-by-Step Solution

To solve the problem, we will expand the expression (a4)(a4)(a-4)(a-4) using the square of a difference formula.

This formula states: (xy)2=x22xy+y2(x-y)^2 = x^2 - 2xy + y^2.
In our case, x=ax = a and y=4y = 4, so we apply the formula:

  • First term: x2=a2x^2 = a^2
  • Second term: 2xy=2a4=8a-2xy = -2 \cdot a \cdot 4 = -8a
  • Third term: y2=42=16y^2 = 4^2 = 16

Putting it all together, the expression becomes:
a28a+16a^2 - 8a + 16.

After matching this result with the given choices, we find it corresponds to choice 4.

Therefore, the solution to the problem is a28a+16\mathbf{a^2 - 8a + 16}.

Answer

a28a+16 a^2-8a+16