Question

(4x+y-9)(4x-y+9)= (a+b+5c)(a+b-5c) =

Answer 1

Ответ:

(4x+y-9)(4x-y+9)=16x²-(y-9)²

16x²-(y²-18y+81)

16x²-y+18y-81

(a+b+5c)(a+b-5c)=(a+b)²-25c²

a²+2ab+b²-25c²

Answer 2

To expand the given expressions, we can use the distributive property and the formula for expanding the product of two binomials (FOIL).

First, let's expand the first expression: (4x + y - 9)(4x - y + 9)

= (4x + y)(4x - y) + (4x + y)(9) - (9)(4x - y) - (9)(9)

Now, apply FOIL to the first two terms:

= (16x^2 - y^2) + (36x + 9y) - (36x - 9y) - 81

Now, combine like terms:

= 16x^2 - y^2 + 36x + 9y - 36x + 9y - 81

Notice that the 36x and -36x terms cancel out:

= 16x^2 - y^2 + 18y - 81

So, the expanded form of the first expression is: 16x^2 - y^2 + 18y - 81

Now, let's expand the second expression: (a + b + 5c)(a + b - 5c)

= (a + b)(a + b) + (a + b)(-5c) + (5c)(a + b) - (5c)(-5c)

Apply FOIL to the first two terms:

= (a^2 + 2ab + b^2) - 5ac + 5ac - 25c^2

Notice that the -5ac and +5ac terms cancel out:

= a^2 + 2ab + b^2 - 25c^2

So, the expanded form of the second expression is: a^2 + 2ab + b^2 - 25c^2

Therefore, the expanded forms of the given expressions are:

1. (4x + y - 9)(4x - y + 9) = 16x^2 - y^2 + 18y - 81
2. (a + b + 5c)(a + b - 5c) = a^2 + 2ab + b^2 - 25c^2