Question

Решите примеры 1) (x+7)^2-(x-7)^2=. 2) (x-5)^2-7= 3) (4a-5b)^2- 16a(a-3b)= 4) (x+4)^2-(x-2)(x+2)= заранее спасибо большое. ПОЖАЛУЙСТА ПОМОГИТЕ.

Answer 1

1)…=используем формулу квадрат разности=(х+7+х-7)(х+7-х+7)=2х*14=28х
2)…=используем формулу разность квадратов=х^2-10х+25-7=х^2-10х+22
3) …=16а^2-40ab+25b^2-16a^2+48ab=25b^2+8ab
4) …=x^2+8x+16-x^2+4=8x+20

Answer 2

Solution:

Let's solve each of the given equations step by step:

1) (x+7)^2 - (x-7)^2 =

To simplify this equation, we can use the difference of squares formula: a^2 - b^2 = (a + b)(a - b).

Applying the formula, we get:

(x+7)^2 - (x-7)^2 = [(x+7) + (x-7)][(x+7) - (x-7)] = [2x + 14][14] = 28x + 196.

Therefore, the simplified form of the equation is 28x + 196.

2) (x-5)^2 - 7 =

To solve this equation, we can expand the square term and simplify:

(x-5)^2 - 7 = (x^2 - 10x + 25) - 7 = x^2 - 10x + 18.

Therefore, the simplified form of the equation is x^2 - 10x + 18.

3) (4a-5b)^2 - 16a(a-3b) =

To solve this equation, we can expand the square term and simplify:

(4a-5b)^2 - 16a(a-3b) = (16a^2 - 40ab + 25b^2) - (16a^2 - 48ab) = 25b^2 + 8ab.

Therefore, the simplified form of the equation is 25b^2 + 8ab.

4) (x+4)^2 - (x-2)(x+2) =

To simplify this equation, we can expand the square term and simplify the product term:

(x+4)^2 - (x-2)(x+2) = (x^2 + 8x + 16) - (x^2 - 4) = x^2 + 8x + 16 - x^2 + 4 = 8x + 20.

Therefore, the simplified form of the equation is 8x + 20.

I hope this helps! Let me know if you have any further questions.