Add or Subtract (Radicals)

{ this means squared

1.3{2 + 4{2 Answer: 7{2

2. 8{3 + 3{3 Answer: 11{3

3. 7{5 - 3{5 Answer: 4{5

4. 8{2 - 5{2 Answer: 3{2

5. 6{x + 7{x Answer: 13{x

6. 9{y + 3{y Answer: 12{y

Multiply

7. -3x^2(4x^2-3x-5) Answer: 12x^2

8.(3b+5)(b-3) Answer: 3b^2-4b-15

9.(6a^2-2)(a^2-1) Answer: -2a^2+2

10. (3p-2)(3p+2) Answer: 9p^2-4

11. (3x^2+4)(3x^2-4) Answer:9x^2-16

12. (x-9)^2 Answer: x^2-18x+81

13. (4x+3)(4x-3) Answer: 16x^2-9

14. (3x^2-2x)^2 Answer: -3x^2+4x

If I got any wrong, can someone please show me how to do them correctly?

check # 7,9,14

#7 is way off, there should have been 3 terms.

do those again.

#7

-3x^2(4x^2-3x-5) just expand
= -12x^4 + 9x^3 + 15x^2

#9
(6a^2-2)(a^2-1)
= 6a^4 - 6a^2 - 2a^2 + 2
= 6a^4 - 8a^2 + 2

#14

(3x^2-2x)^2
= (3x^2 - 2x)(3x^2 - 2x)
= 9x^4 - 6x^3 - 6x^3 + 4x^2
= 9x^4 - 12x^3 + 4x^2

OHHH now I get it!

thank you very much!

I am really lost on all of those 3 problems.

Help please?

y=x2+-24

can u help me

Sure! Let's go through each of the problems one by one and explain how to solve them correctly:

1. To add or subtract radicals, we can only add or subtract them if they have the same radicand (the number inside the square root). In this case, both radicals have the radicand of 2. So, we can combine them by simply adding the coefficients:
1.3{2 + 4{2 = (1.3 + 4){2 = 5.3{2 = 7{2

2. Similar to the first problem, both radicals have the same radicand (3). So, we can combine them:
8{3 + 3{3 = (8 + 3){3 = 11{3

3. Here, the radicands (the numbers inside the square roots) are the same (5). So, we can subtract the coefficients:
7{5 - 3{5 = (7 - 3){5 = 4{5

4. Again, the radicands (2) are the same. We subtract the coefficients:
8{2 - 5{2 = (8 - 5){2 = 3{2

5. This problem involves variables. Since the variables (x) are the same, we can combine the radicals by adding the coefficients:
6{x + 7{x = (6 + 7)x = 13x

6. Similar to the previous problem, we add the coefficients:
9{y + 3{y = (9 + 3)y = 12y

Moving on to the multiplication problems:

7. To multiply, we use the distributive property to multiply each term inside the parentheses with -3x^2:
-3x^2(4x^2 - 3x - 5)
= -3x^2 * 4x^2 - 3x^2 * 3x - 3x^2 * -5
= -12x^4 + 9x^3 + 15x^2
Answer: -12x^4 + 9x^3 + 15x^2

8. We multiply each term from the first parentheses with each term from the second parentheses:
(3b + 5)(b - 3)
= 3b * b + 3b * -3 + 5 * b + 5 * -3
= 3b^2 - 9b + 5b - 15
= 3b^2 - 4b - 15
Answer: 3b^2 - 4b - 15

9. Again, we use the distributive property to multiply each term from the first parentheses with each term from the second parentheses:
(6a^2 - 2)(a^2 - 1)
= 6a^2 * a^2 - 6a^2 * 1 - 2 * a^2 - 2 * -1
= 6a^4 - 6a^2 - 2a^2 + 2
= 6a^4 - 8a^2 + 2
Answer: 6a^4 - 8a^2 + 2

10. We apply the distributive property:
(3p - 2)(3p + 2)
= 3p * 3p + 3p * 2 - 2 * 3p - 2 * 2
= 9p^2 + 6p - 6p - 4
= 9p^2 - 4
Answer: 9p^2 - 4

11. Here, we have a difference of squares, which can be factored using the formula: (a^2 - b^2) = (a + b)(a - b)
(3x^2 + 4)(3x^2 - 4)
= (3x^2)^2 - 4^2
= 9x^4 - 16
Answer: 9x^4 - 16

12. Again, we have a perfect square, which can be expanded using the formula: (a - b)^2 = a^2 - 2ab + b^2
(x - 9)^2 = x^2 - 2(1)(x)(9) + 9^2
= x^2 - 18x + 81
Answer: x^2 - 18x + 81

13. Another difference of squares:
(4x + 3)(4x - 3)
= (4x)^2 - 3^2
= 16x^2 - 9
Answer: 16x^2 - 9

14. Here, we have a binomial squared. We can use the formula: (a - b)^2 = a^2 - 2ab + b^2
(3x^2 - 2x)^2 = (3x^2)^2 - 2(3x^2)(2x) + (2x)^2
= 9x^4 - 12x^3 + 4x^2
Answer: 9x^4 - 12x^3 + 4x^2

I hope this helps you understand how to solve these problems correctly! Let me know if you have any further questions.