Question

(8a-3b)(8a+3b)-(6a-5b)^2

Answer 1

Ответ:

(8a-3b)(8a+3b) = 64a² - 9b²

(64a² - 9b²) - (6a-5b)² = 64a² - 9b² - (36a² - 60ab + 25b²)

64a² - 9b² - 36a² + 60ab - 25b²

28a² + 60ab - 34b²

ответ: 28a² + 60ab - 34b²

Answer 2

To simplify the expression, let's expand each term:

(8a - 3b)(8a + 3b) - (6a - 5b)^2

Expanding the first term using the FOIL method (First, Outer, Inner, Last), we get:

(64a^2 - 9b^2) - (6a - 5b)^2

Now, let's expand the second term:

(64a^2 - 9b^2) - (6a - 5b)(6a - 5b)

Expanding the second term using the FOIL method, we get:

64a^2 - 9b^2 - (36a^2 - 60ab - 60ab + 25b^2)

Simplifying further:

64a^2 - 9b^2 - (36a^2 - 120ab + 25b^2)

Now, distribute the negative sign inside the parentheses:

64a^2 - 9b^2 - 36a^2 + 120ab - 25b^2

Combine like terms:

(64a^2 - 36a^2) + (-9b^2 - 25b^2) + 120ab

28a^2 - 34b^2 + 120ab

So, the simplified form of (8a - 3b)(8a + 3b) - (6a - 5b)^2 is 28a^2 - 34b^2 + 120ab.