Question

(x-7)²; (2x + b)²; (b-3)(b + 3); (5y-2x) (5y + 2x)

Answer 1

Ответ:

(x-7)²=(х-7)*(х-7)=х²-7х-7х+49=х²-14х+49

(2x+b)²=(2х+b)(2x+b)=4x²+2bx+2bx+b²=4x²+4bx+b²

(b-3)*(b+3)=b²+3b-3b-9=b²-9

(5y-2x)*(5y+2x)=25y²+10xy-10xy-4x²=25y²-4x²

Answer 2

1) (x-7)²: To expand this expression, we can use the formula (a-b)² = a² - 2ab + b². So, (x-7)² = x² - 2*7*x + 7² = x² - 14x + 49.

2) (2x + b)²: Using the formula (a+b)² = a² + 2ab + b², we can expand (2x + b)² as follows: (2x + b)² = (2x)² + 2*2x*b + b² = 4x² + 4bx + b².

3) (b-3)(b+3): This expression can be expanded using the formula for the difference of squares, which states that (a-b)(a+b) = a² - b². So, (b-3)(b+3) = b² - 3² = b² - 9.

4) (5y-2x)+(5y+2x): These two terms can be simplified by combining like terms. 5y and 5y are like terms, so when added together, they give 10y. Similarly, -2x and 2x are like terms, so when added together, they give 0. Therefore, the simplified expression is 10y.