Question

(2a+7b)в квадрате (а+3)(а-3) (8х+5у)(5у-8х)

Answer 1

(2a+7b)^2=4a^2+28ab+49b^2

(a+3)(a-3)=a^2-3a+3a-9=a^2-9

(8x+5y)(5y-8x)=40xy-64x^2+25y^2-40xy=25y^2-64x^2

Answer 2

(2a+7b)² = 4a²+28ab+49b²

(а+3)(а-3) = a²-9

(8х+5у)(5у-8х) = 25y² - 64x²

Answer 3

Let's expand the given expressions step by step:

1. (2a + 7b)^2: To expand (2a + 7b)^2, we can use the formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2.

So, in this case, we have (2a + 7b)^2 = (2a)^2 + 2 * 2a * 7b + (7b)^2 = 4a^2 + 28ab + 49b^2.

2. (a + 3)(a - 3): This expression represents the difference of squares (a^2 - b^2), where a = a and b = 3. The formula for the difference of squares is: (a^2 - b^2) = (a + b)(a - b).

So, (a + 3)(a - 3) = a^2 - 3^2 = a^2 - 9.

3. (8x + 5y)(5y - 8x): To expand this expression, we use the distributive property, which states that (a + b)(c + d) = a * c + a * d + b * c + b * d.

(8x + 5y)(5y - 8x) = 8x * 5y + 8x * (-8x) + 5y * 5y + 5y * (-8x) = 40xy - 64x^2 + 25y^2 - 40xy = 25y^2 - 64x^2.

Now, we have the expanded forms of the given expressions:

1. (2a + 7b)^2 = 4a^2 + 28ab + 49b^2.
2. (a + 3)(a - 3) = a^2 - 9.
3. (8x + 5y)(5y - 8x) = 25y^2 - 64x^2.