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.