Question

ДАЮ 100 БАЛЛОВ! упростить выражение: a) (x + 2)(x – 5) -3x(1 - 2x), б) (а + 3)(а - 2) + (a - 3)(a + 6), в) (x - 7)(3x - 2) – (5x + 1)(2x – 4).​

Answer 1

a) (x + 2)(x – 5) -3x(1 - 2x) = х²+2х-5х-10-3х+6х²=7х²-6х-10

б) (а + 3)(а - 2) + (a - 3)(a + 6) = а²+3а-2а-6+а²-3а+6а-18=2а²+4а-24

в) (x - 7)(3x - 2) – (5x + 1)(2x – 4)=3х²-21х-2х+14-10х²-2х+20х+4=-7х²-5х+18

Answer 2

Объяснение:

а)

(х+2)(х-5)-3х(1-2х)=х²-5х+2х-10-3х+6х²=

=7х²-6х-10

б)

(а+3)(а-2)+(а-3)(а+6)=

=а²-2а+3а-6+а²+6а-3а-18=

=2а²+4а-24

в)

(х-7)(3х-2)-(5х+1)(2х-4)=

=3х²-2х-21х+14-(10х²-20х+2х-4)=

=3х²-23х+14-10х²+20х-2х+4=

= -7х²-5х+18

Answer 3

a) (x + 2)(x - 5) - 3x(1 - 2x)

Let's simplify this expression step by step:

Expanding the first part: (x + 2)(x - 5) = x(x) + x(-5) + 2(x) + 2(-5) = x^2 - 5x + 2x - 10 = x^2 - 3x - 10

Expanding the second part: -3x(1 - 2x) = -3x + 6x^2

Now, substituting the expanded expressions back into the original expression: (x^2 - 3x - 10) - (-3x + 6x^2)

Simplifying further: x^2 - 3x - 10 + 3x - 6x^2

Combining like terms: -5x^2 - 10

Therefore, the simplified expression is -5x^2 - 10.

b) (a + 3)(a - 2) + (a - 3)(a + 6)

Expanding the first part: (a + 3)(a - 2) = a(a) + a(-2) + 3(a) + 3(-2) = a^2 - 2a + 3a - 6 = a^2 + a - 6

Expanding the second part: (a - 3)(a + 6) = a(a) + a(6) - 3(a) - 3(6) = a^2 + 6a - 3a - 18 = a^2 + 3a - 18

Now, substituting the expanded expressions back into the original expression: (a^2 + a - 6) + (a^2 + 3a - 18)

Simplifying further: a^2 + a - 6 + a^2 + 3a - 18

Combining like terms: 2a^2 + 4a - 24

Therefore, the simplified expression is 2a^2 + 4a - 24.

c) (x - 7)(3x - 2) - (5x + 1)(2x - 4)

Expanding the first part: (x - 7)(3x - 2) = x(3x) + x(-2) - 7(3x) - 7(-2) = 3x^2 - 2x - 21x + 14 = 3x^2 - 23x + 14

Expanding the second part: (5x + 1)(2x - 4) = 5x(2x) + 5x(-4) + 1(2x) + 1(-4) = 10x^2 - 20x + 2x - 4 = 10x^2 - 18x - 4

Now, substituting the expanded expressions back into the original expression: (3x^2 - 23x + 14) - (10x^2 - 18x - 4)

Simplifying further: 3x^2 - 23x + 14 - 10x^2 + 18x + 4

Combining like terms: -7x^2 - 5x + 18

Therefore, the simplified expression is -7x^2 - 5x + 18.