Multiply using the rule for the square of a binomial: (4x² − 3)².

Step-by-step solution

1. 1

   Recognise the pattern. The expression is a single binomial raised to the second power, so the shortcut $(a-b)^2 = a^2 - 2ab + b^2$ applies. Matching terms gives $a = 4x^2$ and $b = 3$.

2. 2

   Square the first term. $a^2 = (4x^2)^2 = 4^2 \cdot (x^2)^2 = 16x^4$. Both the coefficient and the power get squared — a common slip is to write $4x^4$.

3. 3

   Double the product of the two terms. $2ab = 2 \cdot 4x^2 \cdot 3 = 24x^2$. Because the binomial has a minus sign, this middle term is subtracted.

4. 4

   Square the last term. $b^2 = 3^2 = 9$. Squaring removes the sign, so the constant is positive even though the original term was $-3$.

5. 5

   Assemble the trinomial. Putting the three pieces together in descending powers gives $16x^4 - 24x^2 + 9$.

6. 6

   Check with one value. At $x = 1$ the original is $(4-3)^2 = 1$ and the expansion is $16 - 24 + 9 = 1$, so the two agree.