Please perform the indicated operations and simplify

(3x-5)^2-(2x+1)(x-4)

(3x-5)^2-(2x+1)(x-4)

use FOIL to expand each one

= 9x^2 - 30x + 25 - (2x^2 - 8x + x - 4)

now simplify

Yes but doesn't -8x and x combine to become -7x? so then it should look like this?

-2x^2 -7x -4?

of course ...

that is what I meant by simplify.

I was expecting you to finish the question.

can you tell me what the next few lines would be ?

9x2-30x+25

-2x2 -7x -4
--------------
7x2 -23+29
Is this correct?

Thanks Breanna! Looks correct to me!

Perform the indicated operations and simplify (2x - 6) (x + 1) - (x - 7)^2

To simplify the given expression (3x - 5)^2 - (2x + 1)(x - 4), we will start by expanding both squared terms and the product of the binomials. Let's break it down step by step:

Step 1: Expand (3x - 5)^2

To expand a squared binomial, we apply the formula (a - b)^2 = a^2 - 2ab + b^2.

Here, a = 3x, and b = 5. Applying the formula:

(3x - 5)^2 = (3x)^2 - 2(3x)(5) + (5)^2
= 9x^2 - 30x + 25

Step 2: Expand (2x + 1)(x - 4)

To expand the product of two binomials, we use the distributive property. Multiply each term of the first binomial by each term of the second binomial.

(2x + 1)(x - 4) = 2x(x - 4) + 1(x - 4)
= 2x^2 - 8x + x - 4
= 2x^2 - 7x - 4

Step 3: Substitute the expanded terms back into the original expression

Now that we have expanded both terms, we substitute them back into the original expression:

(3x - 5)^2 - (2x + 1)(x - 4) = (9x^2 - 30x + 25) - (2x^2 - 7x - 4)

Step 4: Simplify the expression by combining like terms

Distribute the negative sign to every term within the second parentheses:

= 9x^2 - 30x + 25 - 2x^2 + 7x + 4

Combine like terms:

= (9x^2 - 2x^2) + (-30x + 7x) + (25 + 4)
= 7x^2 - 23x + 29

So, the simplified form of (3x - 5)^2 - (2x + 1)(x - 4) is 7x^2 - 23x + 29.