Simplify the following (6b-2)(6b+2)+4(b^2-3b)
Find the factors of the following
e^2+8e+15
5f^2-15f+10
Does g^2-9 have factors? If so, how there is no "middle" term?
expand it first
(6b-2)(6b+2)+4(b^2-3b)
= 36b^2 - 4 + 4b^2 - 12b
= 40b^2 - 12b - 4
e^2 + 8e + 15
-- can you think of two numbers that add up to 8, and multiply to get 15 ?
5f^2 - 15f + 10
= 5(f^2 - 3f + 2)
= 5(f-1)(f-2)
g^2 - 9
is the difference of squares, you should know that one.
look at the two factors at the front of your first question and what happened when I expanded it.
Can you reverse the process?
(6b-2)(6b+2) +4(b^2-3b)
= 36b^2 -4 +4b^2 -12b
= 40b^2 -12b -4
= 4(10b^2 -3b -1)
= 4(5b -1)(2b + 1)
I don't what would be considered the simplets form.
e^2 +8e +15 = (e+3)(e+5)
5f^2 -15f +10 = 5(f^2 -3f +2)
= 5(f-1)(f-2)
Does g^2-9 have factors?
yes. (g-3)(g+3)
The middle terms can cancel whenever you have the difference of two squares.
To simplify the expression (6b-2)(6b+2)+4(b^2-3b), we can use the distributive property to expand both sets of parentheses and then combine like terms.
First, let's expand the first set of parentheses:
(6b-2)(6b+2) = 6b * 6b + 6b * 2 - 2 * 6b - 2 * 2
= 36b^2 + 12b - 12b - 4
= 36b^2 - 4
Next, let's expand the second set of parentheses:
4(b^2-3b) = 4 * b^2 - 4 * 3b
= 4b^2 - 12b
Now, we can combine the simplified expressions:
(6b-2)(6b+2)+4(b^2-3b) = 36b^2 - 4 + 4b^2 - 12b
= 40b^2 - 12b - 4
So, the simplified form of (6b-2)(6b+2)+4(b^2-3b) is 40b^2 - 12b - 4.
To find the factors of the quadratic expression e^2 + 8e + 15, we need to factor it into two binomials.
The factors of e^2 + 8e + 15 can be found by finding two numbers that multiply to give 15 and add up to 8 (the coefficient of the middle term).
In this case, the factors of 15 are 3 and 5, and they add up to 8 (3 + 5 = 8).
Therefore, the factored form of e^2 + 8e + 15 is (e + 3)(e + 5).
Similarly, to find the factors of the quadratic expression 5f^2 - 15f + 10, we look for two numbers that multiply to give 10 and add up to -15 (the coefficient of the middle term).
In this case, the factors of 10 are 2 and 5, and they add up to -15 (2 + 5 = -15).
Therefore, the factored form of 5f^2 - 15f + 10 is 5(f - 2)(f - 5).
Lastly, for the expression g^2 - 9, it can be factored as a difference of squares. The expression is in the form of a^2 - b^2, where a is g and b is 3.
The factored form of g^2 - 9 becomes (g - 3)(g + 3).
Even though there is no "middle" term, the expression g^2 - 9 can still be factored as it follows the pattern for the difference of squares.