Question 1:
For this case we must simplify the following expression:
[tex](6k-k ^ 2 + 6) - (5 + 7k + 6k ^ 2) - (1 + 3k ^ 2-4k)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\6k-k ^ 2 + 6-5-7k-6k ^ 2-1-3k ^ 2 + 4k =[/tex]
We group similar terms:
[tex]-k ^ 2-6k ^ 2-3k ^ 2 + 6k-7k + 4k + 6-5-1 =[/tex]
We take into account that:
Same signs add up and the same sign is placed
Different signs are subtracted and the major sign is placed
[tex]-10k ^ 2 + 3k + 0 =\\-10k ^ 2 + 3k[/tex]
Answer:
[tex]-10k ^ 2 + 3k[/tex]
Question 2:
For this case we must simplify the following expression:
[tex](5a^4-2a^2-6a^3)+(2a-3a^3-a^4)-(7a+6a^4-5a^3)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\5a^4-2a^2-6a^3+2a-3a^3-a^4-7a-6a^4+5a^3=[/tex]
We group similar terms:
[tex]5a^4-a^4-6a^4-6a^3-3a^3+5a^3-2a^2+2a-7a=[/tex]
We take into account that:
Same signs add up and the same sign is placed
Different signs are subtracted and the major sign is placed
[tex]-2a ^ 4-4a ^ 3-2a ^ 2-5a[/tex]
Answer:
[tex]-2a ^ 4-4a ^ 3-2a ^ 2-5a[/tex]
Question 3:
For this case we must simplify the following expression:
[tex](3k ^ 4 + k ^ 2-5 + 3k) + (1-5k + 4k ^ 4-8k ^ 3) + (5 + k ^ 2-3k ^ 4 + 3k)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\3k ^ 4 + k ^ 2-5 + 3k + 1-5k + 4k ^ 4-8k ^ 3 + 5 + k ^ 2-3k ^ 4 + 3k =[/tex]
We group similar terms:
[tex]3k ^ 4 + 4k ^ 4-3k ^ 4-8k ^ 3 + k ^ 2 + k ^ 2 + 3k-5k + 3k-5 + 1 + 5 =[/tex]
We take into account that:
Same signs add up and the same sign is placed
Different signs are subtracted and the major sign is placed
[tex]4k ^ 4-8k ^ 3 + 2k ^ 2 + k + 1[/tex]
ANswer:
[tex]4k ^ 4-8k ^ 3 + 2k ^ 2 + k + 1[/tex]
Question 4:
For this case we must simplify the following expression:
[tex](4v-7-7v ^ 2-5v ^ 4) + (2v ^ 3-4 + 2v-8v ^ 2) + (8v-6v ^ 3-1 + 4v ^ 2)[/tex]
We eliminate the parentheses taking into account that:
[tex]- * + = -\\- * - = +\\4v-7-7v ^ 2-5v ^ 4 + 2v ^ 3-4 + 2v-8v ^ 2 + 8v-6v ^ 3-1 + 4v ^ 2 =[/tex]
We group similar terms:
[tex]-5v ^ 4 + 2v ^ 3-6v ^ 3-7v ^ 2-8v ^ 2 + 4v ^ 2 + 4v + 2v + 8v-7-4-1 =[/tex]
We take into account that:
Same signs add up and the same sign is placed
Different signs are subtracted and the major sign is placed
[tex]-5v ^ 4-4v ^ 3-11v ^ 2 + 14v-12[/tex]
Answer:
[tex]-5v ^ 4-4v ^ 3-11v ^ 2 + 14v-12[/tex]
Question 5:
For this case we have that by definition, the perimeter of the triangle will be given by the sum of its sides. That is to say:
[tex]3x ^ 2-7x + 2 = (2x ^ 2-10x + 6) + (x ^ 2-x-4) + AC[/tex]
We simplify the right side of the equation:
[tex]3x ^ 2-7x + 2 = 2x ^ 2-10x + 6 + x ^ 2-x-4 + AC\\3x ^ 2-7x + 2 = 3x ^ 2-11x + 4 + AC[/tex]
We cleared AC:
[tex]AC = 3x ^ 2-7x + 2- (3x ^ 2-11x + 4)\\- * + = -\\- * - = +\\AC = 3x ^ 2-7x + 2-3x ^ 2 + 11x-4\\AC = 4x-2[/tex]
Answer:
[tex]AC = 4x-2[/tex]
