Question

Раскройте скобки а)(2x+y)²-(2x-y)² б)(c-(a+b))²​

Answer 1

а) разность квадратов:

(2х+у+2х-у)(2х+у-2х+у)=4х*2у=8ху

б) квадрат разности:

(с-(а+в))²=с²-2с(а+в)+(а+в)²=

с²-2ас-2вс+а²+2ав+в²=с²+а²+в²-2ас-2вс+2ав.

Answer 2

a) (2x+y)² - (2x-y)²

Let's expand the expression step by step:

(2x+y)² = (2x+y)(2x+y) = 4x² + 2xy + 2xy + y² = 4x² + 4xy + y²

(2x-y)² = (2x-y)(2x-y) = 4x² - 2xy - 2xy + y² = 4x² - 4xy + y²

Now, let's substitute the expanded expressions back into the original expression:

(2x+y)² - (2x-y)² = (4x² + 4xy + y²) - (4x² - 4xy + y²) = 4x² + 4xy + y² - 4x² + 4xy - y² = 8xy

Therefore, (2x+y)² - (2x-y)² simplifies to 8xy.

b) (c-(a+b))²

Let's expand the expression step by step:

(c - (a+b))² = (c - a - b)²

To expand this expression, we can use the formula for squaring a binomial:

(a - b)² = a² - 2ab + b²

Applying the formula to our expression:

(c - a - b)² = c² - 2c(a + b) + (a + b)² = c² - 2c(a + b) + a² + 2ab + b²

Therefore, (c-(a+b))² expands to c² - 2c(a + b) + a² + 2ab + b².