Question

Представить в виде многочлена выражение: 1). 3х(х -4х+6)= 3 2). (х-3)(2х+1)= 3). (4а-7в)(5а+6в)= 4). (у+2)(у +у-8)=

Answer 1

Ответ:

3x²-12x²+18x=-9х²+18х

2x²+x-6x-3=2x²-5x-3

20a²+24ab-35ab-42b²=20a²-11ab-42b²

y²+y²-8y+2y+2y²-16=4y²-6y-16

Answer 2

1. 3x(x - 4x + 6) can be simplified and expressed as a polynomial:

First, combine like terms within the parentheses: 3x(-3x + 6)

Then distribute the 3x to both terms inside the parentheses: 3x * -3x + 3x * 6

Simplifying further: -9x^2 + 18x

So the expression 3x(x - 4x + 6) can be represented as the polynomial -9x^2 + 18x.

2. (x - 3)(2x + 1) can also be expanded and represented as a polynomial:

Using the FOIL method (First, Outer, Inner, Last), multiply the corresponding terms within the parentheses: x * 2x + x * 1 - 3 * 2x - 3 * 1

Simplifying: 2x^2 + x - 6x - 3

Combining like terms: 2x^2 - 5x - 3

Therefore, the expression (x - 3)(2x + 1) is equivalent to the polynomial 2x^2 - 5x - 3.

3. (4a - 7b)(5a + 6b) can also be expanded:

Using the FOIL method: 4a * 5a + 4a * 6b - 7b * 5a - 7b * 6b

Simplifying: 20a^2 + 24ab - 35ab - 42b^2

Combining like terms: 20a^2 - 11ab - 42b^2

Thus, (4a - 7b)(5a + 6b) can be represented as the polynomial 20a^2 - 11ab - 42b^2.

4. (y + 2)(y + y - 8) can be simplified and expressed as a polynomial:

First, combine like terms within the parentheses: (y + 2)(2y - 8)

Using the FOIL method: y * 2y + y * -8 + 2 * 2y + 2 * -8

Simplifying: 2y^2 - 8y + 4y - 16

Combining like terms: 2y^2 - 4y - 16

Therefore, (y + 2)(y + y - 8) is equivalent to the polynomial 2y^2 - 4y - 16.