1- Subtract (7a^2 - 3a) - (5a^2 - 5a)
a) 2a^2 + 2a
b) 2a^2 - 8a**
c) 12a^2 - 8a
d) 12a^2 + 2a
2- Is x(4x^2 - 16) completely factored? If not, how else can it be factored?
a) no; 4 can be factored from each term of the binomial AND the resulting binomial is a difference of two squares that factors into two binomials.
b) no; the binomial is a difference of two squares and can be factored into two binomials.
c) no; 4 can be factored from each term of the binomial.**
d) yes; the polynomial is completely factored.
3- Determine whether p^2 - 40 is a difference of two squares. If so, choose the correct factoring.
a) yes; (x - 20)^2
b) yes; (x - 10)^4
c) yes; (x + 4) (x - 10)**
d) no
PLEASE HELP ASAP :)
1- To subtract (7a^2 - 3a) - (5a^2 - 5a), we need to distribute the negative sign across the terms inside the second parentheses:
= 7a^2 - 3a - 5a^2 + 5a
Next, we combine like terms by adding or subtracting the coefficients of the same powers of 'a':
= (7a^2 - 5a^2) + (-3a + 5a)
= 2a^2 + 2a
Therefore, the correct answer is option a) 2a^2 + 2a.
2- To determine if x(4x^2 - 16) is completely factored, we need to check if any further factoring is possible.
First, we can factor out the common factor of 4 from each term inside the parentheses:
= x * 4(x^2 - 4)
Next, we observe that the expression inside the parentheses can be further factored because it represents the difference of two squares. The formula for factoring the difference of two squares is a^2 - b^2 = (a + b)(a - b). In this case, a = x and b = 2:
= x * 4(x + 2)(x - 2)
Therefore, the correct answer is option c) no; 4 can be factored from each term of the binomial.
3- To determine if p^2 - 40 is a difference of two squares, we need to check if the expression can be written in the form a^2 - b^2.
In this case, p^2 - 40 does not have a perfect square term subtracted from another perfect square term. Hence, it is not a difference of two squares.
Therefore, the correct answer is option d) no.
0 for 3
1 ... distributing the minus ... 7a^2 - 3a - 5a^2 + 5a
... combine like terms
2 ... after factoring out the 4 , the difference of two squares is remaining
3 ... 40 is not a perfect square (not a whole number root)
1. nope
(7a^2 - 3a) - (5a^2 - 5a)
= 7a^2 - 3a - 5a^2 + 5a
=
2. nope
I see a common factor followed by a difference of squares in
4x^2 - 16
= 4(x^2 - 4)
= 4(x-2)(x+2) , don't forget the x in front
3. 40 would have to be a perfect square. It is not