Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

1. Simplify the following expressions:

a) [tex]\((3x + 4)^2 =\)[/tex]

b) [tex]\((2x + 4)(2x - 6) =\)[/tex]

Sagot :

GinnyAnswer
Certainly! Let's go through each part step-by-step.

### Part a: Expand [tex]\((3x + 4)^2\)[/tex]

To expand [tex]\((3x + 4)^2\)[/tex], you can use the formula for the square of a binomial: [tex]\((a + b)^2 = a^2 + 2ab + b^2\)[/tex].

In this case, [tex]\(a = 3x\)[/tex] and [tex]\(b = 4\)[/tex].

So, we have:
[tex]\[ (3x + 4)^2 = (3x)^2 + 2 \cdot (3x) \cdot 4 + 4^2 \][/tex]

Now, calculate each term:
- [tex]\((3x)^2 = 9x^2\)[/tex]

- [tex]\(2 \cdot (3x) \cdot 4 = 2 \cdot 3 \cdot 4 \cdot x = 24x\)[/tex]

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

Putting it all together:
[tex]\[ (3x + 4)^2 = 9x^2 + 24x + 16 \][/tex]

### Part b: Expand [tex]\((2x + 4)(2x - 6)\)[/tex]

To expand [tex]\((2x + 4)(2x - 6)\)[/tex], you can use the distributive property (also known as the FOIL method for binomials).

[tex]\[ (2x + 4)(2x - 6) = 2x(2x) + 2x(-6) + 4(2x) + 4(-6) \][/tex]

Now, calculate each term:
- [tex]\(2x \cdot 2x = 4x^2\)[/tex]

- [tex]\(2x \cdot (-6) = -12x\)[/tex]

- [tex]\(4 \cdot 2x = 8x\)[/tex]

- [tex]\(4 \cdot (-6) = -24\)[/tex]

Now, combine like terms:
[tex]\[ (2x + 4)(2x - 6) = 4x^2 - 12x + 8x - 24 \][/tex]

Combining [tex]\(-12x\)[/tex] and [tex]\(8x\)[/tex]:
[tex]\[ 4x^2 - 12x + 8x - 24 = 4x^2 - 4x - 24 \][/tex]

### Final Answer:

a) [tex]\((3x + 4)^2 = 9x^2 + 24x + 16\)[/tex]

b) [tex]\((2x + 4)(2x - 6) = 4x^2 - 4x - 24\)[/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.