Question

представьте в виде многочлена выражений: 1) (m-4)2 2) (3a+6b)2 3) (a+4)(a-4) 4) (6x+7y) (7y-6x)

Answer 1

Ответ:

1) 2m-8

2) 6a+12b

3) a^2-16

4) 49y^2-36x^2

Объяснение:

Answer 2

1. (m-4)^2

To expand this expression, we'll use the formula for squaring a binomial: (a - b)^2 = a^2 - 2ab + b^2

In our case, a = m and b = 4:

(m - 4)^2 = m^2 - 2(m)(4) + 4^2 = m^2 - 8m + 16

So the expanded form of the expression is: m^2 - 8m + 16

2. (3a + 6b)^2

Using the same formula for squaring a binomial: (a + b)^2 = a^2 + 2ab + b^2

Here, a = 3a and b = 6b:

(3a + 6b)^2 = (3a)^2 + 2(3a)(6b) + (6b)^2 = 9a^2 + 36ab + 36b^2

The expanded form of the expression is: 9a^2 + 36ab + 36b^2

3. (a + 4)(a - 4)

To expand this expression, we'll use the formula for multiplying binomials: (a + b)(a - b) = a^2 - b^2

In our case, a = a and b = 4:

(a + 4)(a - 4) = a^2 - 4^2 = a^2 - 16

The expanded form of the expression is: a^2 - 16

4. (6x + 7y)(7y - 6x)

To expand this expression, we'll use the distributive property:

(6x + 7y)(7y - 6x) = 6x * 7y + 6x * (-6x) + 7y * 7y + 7y * (-6x)

Now, simplify each term:

= 42xy - 36x^2 + 49y^2 - 42xy

The "42xy" terms cancel out, leaving us with:

= -36x^2 + 49y^2

The expanded form of the expression is: -36x^2 + 49y^2