How do you solve the following problems? I get confused, can anyone help? Thanks.
(7a^5-a^3)-(a^5-5a^3-1)
(5x-3)(x^3-5x+2)
(4w+5z)^2
does it tell you what the variables represent?
for addition and subtraction, just collect terms with the same power
(7a^5-a^3)-(a^5-5a^3-1)
7a^5-a^3-a^5+5a^3+1)
(7-1)a^5 + (-1+5)a^3 + 1
4a^5 + 4a^3 + 1
When multiplying, use the distributive property
(5x-3)(x^3-5x+2)
(5x)(x^3-5x+2) - 3(x^3-5x+2)
5x^4-25x^2+10x-3x^3+15x-6
5x^4-3x^3-25x^2+25x-6
You can do the squared binomial as the one above, or recall that
(a+b)^2 = a^2 + 2ab + b^2
so, you have
(4w+5z)^2
= (4w)^2 + 2(4w)(5z) + (5z)^2
= 16w^2 + 40wx + 25z^2
No it does not tell you what the variables represent.
I'm still a little confused but thank you Steve for your help. :)
Sure, I'd be happy to help! Let's go through each problem step by step.
1. (7a^5 - a^3) - (a^5 - 5a^3 - 1):
To solve this problem, we need to simplify and combine like terms. Start by distributing the negative sign through the parentheses in the second term:
7a^5 - a^3 - a^5 + 5a^3 + 1
Now, combine like terms:
(7a^5 - a^5) + (-a^3 + 5a^3) + 1
6a^5 + 4a^3 + 1
So, the answer is 6a^5 + 4a^3 + 1.
2. (5x - 3)(x^3 - 5x + 2):
To solve this problem, we can use the distributive property to expand the expression. Multiply each term of the first binomial by each term of the second binomial:
5x * x^3 + 5x * (-5x) + 5x * 2 - 3 * x^3 - 3 * (-5x) - 3 * 2
Simplify each term:
5x^4 - 25x^2 + 10x - 3x^3 + 15x - 6
Now, combine like terms:
5x^4 - 3x^3 - 25x^2 + 25x - 6
So, the answer is 5x^4 - 3x^3 - 25x^2 + 25x - 6.
3. (4w + 5z)^2:
To solve this problem, we need to multiply the entire expression by itself. Start by using the FOIL method (First, Outer, Inner, Last) to multiply each term in the first binomial by each term in the second binomial:
(4w)^2 + 2(4w)(5z) + (5z)^2
Simplify each term:
16w^2 + 40wz + 25z^2
So, the answer is 16w^2 + 40wz + 25z^2.
I hope this helps! Let me know if you have any further questions.