Expand (4b-3)(4b-3): Converting to Perfect Square Form

Question

(4b3)(4b3) (4b-3)(4b-3)

Rewrite the above expression as an exponential summation expression:

Video Solution

Solution Steps

00:00 Express the expression as a power expression and as a sum
00:03 A factor multiplied by itself is essentially squared
00:13 Therefore the parentheses are squared
00:19 We'll use the shortened multiplication formulas to expand the parentheses
00:38 Let's calculate the squares and products
00:56 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we will apply the square of a binomial formula.

The given expression is (4b3)(4b3)(4b-3)(4b-3). We recognize this as the square of a binomial, which can be rewritten as (4b3)2(4b-3)^2. To expand this expression, we use the formula:

(ab)2=a22ab+b2(a-b)^2 = a^2 - 2ab + b^2

In our expression, a=4ba = 4b and b=3b = 3. Let's apply the formula:

  • Calculate a2a^2:
    a2=(4b)2=16b2a^2 = (4b)^2 = 16b^2
  • Calculate 2ab-2ab:
    2ab=2(4b)(3)=24b-2ab = -2(4b)(3) = -24b
  • Calculate b2b^2:
    b2=(3)2=9b^2 = (3)^2 = 9

Putting it all together, we have:

(4b3)2=16b224b+9(4b-3)^2 = 16b^2 - 24b + 9

Therefore, the exponential summation expression is (4b3)2(4b-3)^2, with the expanded form:

16b224b+916b^2 - 24b + 9

This matches choice 3, confirming our solution.

Answer

(4b3)2 (4b-3)^2

16b224b+9 16b^2-24b+9