Question

(x-7)^2=? (2x^2+5)^2=? (8x^2+9)(8x^2-9)=? (x^2-3y^3)^2=? (x-6) (x+6)=?

Answer 1

(x-7)^2=x^2-28x+49

(2x^2+5)^2=4x^2+20x+25

(8x^2+9)(8x^2-9)=64x^4-81

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

(x-6)(x+6)=x^2-36

Answer 2

Let's go through each of the expressions one by one:

1. (x - 7)^2: Expanding the square of a binomial follows the formula: (a - b)^2 = a^2 - 2ab + b^2. In this case, a = x and b = 7. Plugging these values into the formula:

   (x - 7)^2 = x^2 - 2 * x * 7 + 7^2 = x^2 - 14x + 49.

2. (2x^2 + 5)^2: Using the same formula as above with a = 2x^2 and b = 5:

   (2x^2 + 5)^2 = (2x^2)^2 - 2 * 2x^2 * 5 + 5^2 = 4x^4 - 20x^2 + 25.

3. (8x^2 + 9)(8x^2 - 9): This is a difference of squares, which follows the formula: (a + b)(a - b) = a^2 - b^2. In this case, a = 8x^2 and b = 9. Plugging these values into the formula:

   (8x^2 + 9)(8x^2 - 9) = (8x^2)^2 - 9^2 = 64x^4 - 81.

4. (x^2 - 3y^3)^2: This is the square of a binomial again, with a = x^2 and b = -3y^3:

   (x^2 - 3y^3)^2 = (x^2)^2 - 2 * x^2 * 3y^3 + (-3y^3)^2 = x^4 - 6x^2y^3 + 9y^6.

5. (x - 6)(x + 6): This is a difference of squares again, with a = x and b = 6:

   (x - 6)(x + 6) = x^2 - 6^2 = x^2 - 36.

Please note that these expressions have been simplified using basic algebraic techniques.