Answered

Experience the power of community-driven knowledge on IDNLearn.com. Ask any question and get a thorough, accurate answer from our community of experienced professionals.

[tex]\[
\begin{array}{l}
\text{6. } (x-4)(x+4) = \\
\text{7. } (2r-5)(2r-5) = \\
\text{8. } (3-4m^2) = \\
\text{9. } 9 \cdot (2h+7)(2h-7) = \\
\text{10. } (8-3x)(8+3y) =
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's break down each of these expressions step-by-step and solve them:

### 6. [tex]\((x-4)(x+4)\)[/tex]

This is a classic difference of squares problem. The formula for the difference of squares is:

[tex]\[ (a - b)(a + b) = a^2 - b^2 \][/tex]

In this case, [tex]\(a = x\)[/tex] and [tex]\(b = 4\)[/tex]. Applying the formula, we get:

[tex]\[ (x - 4)(x + 4) = x^2 - 4^2 = x^2 - 16 \][/tex]

So, the expanded form is:

[tex]\[ x^2 - 16 \][/tex]

### 7. [tex]\((2r-5)(2r-5)\)[/tex]

This problem involves squaring a binomial. The formula for the square of a binomial is:

[tex]\[ (a - b)^2 = a^2 - 2ab + b^2 \][/tex]

Here, [tex]\(a = 2r\)[/tex] and [tex]\(b = 5\)[/tex]. Applying the formula, we get:

[tex]\[ (2r - 5)^2 = (2r)^2 - 2 \cdot 2r \cdot 5 + 5^2 = 4r^2 - 20r + 25 \][/tex]

So, the expanded form is:

[tex]\[ 4r^2 - 20r + 25 \][/tex]

### x. [tex]\((3 - 4m^2)\)[/tex]

This expression is already in its simplest form, and no expansion is needed. The expression remains:

[tex]\[ 3 - 4m^2 \][/tex]

### 9. [tex]\((2h+7)(2h-7)\)[/tex]

Again, this is a difference of squares problem. Using the formula:

[tex]\[ (a - b)(a + b) = a^2 - b^2 \][/tex]

We have [tex]\(a = 2h\)[/tex] and [tex]\(b = 7\)[/tex]. Applying the formula, we get:

[tex]\[ (2h + 7)(2h - 7) = (2h)^2 - 7^2 = 4h^2 - 49 \][/tex]

So, the expanded form is:

[tex]\[ 4h^2 - 49 \][/tex]

### 10. [tex]\((8 - 3x)(8 + 3y)\)[/tex]

This expression requires a straightforward distribution (also known as the FOIL method). Multiply each term in the first binomial by each term in the second binomial:

[tex]\[ (8 - 3x)(8 + 3y) = 8 \cdot 8 + 8 \cdot 3y - 3x \cdot 8 - 3x \cdot 3y \][/tex]

Simplifying each product, we get:

[tex]\[ = 64 + 24y - 24x - 9xy \][/tex]

So, the expanded form is:

[tex]\[ 64 + 24y - 24x - 9xy \][/tex]

### Summary of Solutions

[tex]\[ \begin{array}{l} 6. \quad (x - 4)(x + 4) = x^2 - 16 \\ 7. \quad (2r - 5)(2r - 5) = 4r^2 - 20r + 25 \\ x. \quad 3 - 4m^2 \\ 9. \quad (2h + 7)(2h - 7) = 4h^2 - 49 \\ 10. \quad (8 - 3x)(8 + 3y) = 64 + 24y - 24x - 9xy \\ \end{array} \][/tex]

These are the detailed, step-by-step solutions to the given problems!
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.