The formula for the difference of squares

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

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

$(a-b)^2 = a^2 - 2ab + b^2$

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

• Calculate $a^2$:
  $a^2 = (4b)^2 = 16b^2$
• Calculate $-2ab$:
  $-2ab = -2(4b)(3) = -24b$
• Calculate $b^2$:
  $b^2 = (3)^2 = 9$

Putting it all together, we have:

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

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

$16b^2 - 24b + 9$

This matches choice 3, confirming our solution.

To solve this problem, let's start by identifying the parts of the binomial:

• The expression $(3x-y)^2$ represents a binomial squared.
• We recognize it has the form $(a-b)^2$ where $a = 3x$ and $b = y$.
• Using the formula for the square of a difference: $(a-b)^2 = a^2 - 2ab + b^2$, we find the expanded form.

Let's apply the formula:

Step 1: Expand $(3x-y)^2$ using the formula:
$(3x-y)^2 = (3x)^2 - 2(3x)(y) + y^2$

Step 2: Calculate each part:
$(3x)^2 = 9x^2$
$-2(3x)(y) = -6xy$
$y^2$ stays as $y^2$

Step 3: Combine these results to get the addition form:
$9x^2 - 6xy + y^2$

The expression in multiplication form, as provided, is just repeating the factors:
$(3x-y)(3x-y)$

Therefore, the expression rewritten as addition is $9x^2 - 6xy + y^2$ and as multiplication $(3x-y)(3x-y)$.

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

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

• First term: $x^2 = a^2$
• Second term: $-2xy = -2 \cdot a \cdot 4 = -8a$
• Third term: $y^2 = 4^2 = 16$

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

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

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

To solve for $(7b - 3x)^2$ as a sum, we'll follow these steps:

• Step 1: Identify the given expression and apply the formula for the square of a difference:
  $(a - b)^2 = a^2 - 2ab + b^2$ where $a = 7b$ and $b = 3x$.
• Step 2: Expand each term:
• $a^2 = (7b)^2 = 49b^2$
• $-2ab = -2 \times 7b \times 3x = -42bx$
• $b^2 = (3x)^2 = 9x^2$
• Step 3: Combine all terms to form the sum:
  $(7b - 3x)^2 = 49b^2 - 42bx + 9x^2$.

Therefore, the solution to the problem is $(7b - 3x)^2 = 49b^2 - 42bx + 9x^2$.

Hence, the correct answer choice is: $49b^2 - 42bx + 9x^2$

We use the abbreviated multiplication formula:

$(x-y)(x-y)=$

$x^2-xy-yx+y^2=$

$x^2-2xy+y^2$