Question

1) (2a+5)^2-49 2) (5x-2y)^2-9y^2 3) (2a+b)^2-(a-b)^2

Answer 1

= (2а+5+7)(2а+5-7)=(2а+12)(2а-2)=4(а+6)(а-1)
= (5х-2у+3у)(5х-2у-3у)=(5х+у)(5х-5у)=5(5х+у)(х-у)
= (2а+в+а-в)(2а+в-а+в)=3а(а-2в)

Answer 2

Let's simplify each of the given expressions:

1. $(2a+5)^2 - 49$

To simplify this expression, first expand the square:

$(2a+5)^2 = 4a^2 + 20a + 25$

Now subtract 49:

$4a^2 + 20a + 25 - 49$

Combine like terms:

$4a^2 + 20a - 24$

Now, you can factor out a 4 from the terms with 'a':

$4(a^2 + 5a - 6)$

Now, factor the quadratic inside the parentheses:

$4(a + 6)(a - 1)$

So, $(2a+5)^2 - 49$ simplifies to $4(a + 6)(a - 1)$.

2. $(5x-2y)^2 - 9y^2$

First, expand the square:

$(5x-2y)^2 = 25x^2 - 20xy + 4y^2$

Now, subtract $9y^2$:

$25x^2 - 20xy + 4y^2 - 9y^2$

Combine like terms:

$25x^2 - 20xy - 5y^2$

Now, you can factor out a common factor of 5:

$5(5x^2 - 4xy - y^2)$

3. $(2a+b)^2 - (a-b)^2$

First, expand both squares:

$(2a+b)^2 = 4a^2 + 4ab + b^2$ $(a-b)^2 = a^2 - 2ab + b^2$

Now subtract the second expression from the first:

$(4a^2 + 4ab + b^2) - (a^2 - 2ab + b^2)$

Distribute the negative sign when subtracting:

$4a^2 + 4ab + b^2 - a^2 + 2ab - b^2$

Combine like terms:

$4a^2 - a^2 + 4ab + 2ab + b^2 - b^2$

$3a^2 + 6ab$

So, $(2a+b)^2 - (a-b)^2$ simplifies to $3a^2 + 6ab$.