Short Multiplication Formulas - Examples, Exercises and Solutions

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: $49b^2 - 42bx + 9x^2$

To solve the expression $(x-x^2)^2$, we will use the square of a binomial formula $(a-b)^2 = a^2 - 2ab + b^2$.

Let's identify $a$ and $b$ in our expression:

• Here, $a = x$ and $b = x^2$.

Applying the formula:

$(x - x^2)^2 = (x)^2 - 2(x)(x^2) + (x^2)^2$

Calculating each part, we get:

• $(x)^2 = x^2$
• $-2(x)(x^2) = -2x^3$
• $(x^2)^2 = x^4$

Combining these results, the expression simplifies to:

$x^4 - 2x^3 + x^2$

Therefore, the expanded form of $(x-x^2)^2$ is $\boxed{x^4 - 2x^3 + x^2}$.

To solve the problem, we need to expand the expression $(x-7)^2$ using the formula for the square of a difference.

The formula for the square of a difference is $(a-b)^2 = a^2 - 2ab + b^2$.

Let's apply this formula to our expression $(x-7)^2$:

• Identify $a = x$ and $b = 7$.
• Substitute these values into the formula: $(x-7)^2 = x^2 - 2(x)(7) + 7^2$.
• Calculate each term:
• $x^2$ remains as $x^2$.
• $-2(x)(7) = -14x$.
• $7^2 = 49$.

So, expanding the expression, we get $x^2 - 14x + 49$.

Thus, the expression that has the same value as $(x-7)^2$ is $x^2 - 14x + 49$.

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 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 $(3x-y)(3x-y)$.