Question

Умножение многочлена на многочлен 1) (x+y)(x-y)2) (x+2)(y-6)3) (4-a)(5-b)4) (a-2)(3-a)5) (2x-1)(3+4x)1. 4x-(x-1)(x+3)2. a²-(a+b)(a-2b)3. 20+(4-x)(x-5)4. (3x-5)(x+1)-3x²5. (-4x+6)(-x-2)-4x²​

Answer 1

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Answer 2

To multiply the given polynomials, you can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Let's go through each multiplication step-by-step:

1. (x + y)(x - y)

Apply FOIL: First: x * x = x^2 Outer: x * (-y) = -xy Inner: y * x = xy Last: y * (-y) = -y^2

Combine the terms: Result: x^2 - xy + xy - y^2

Simplify: Result: x^2 - y^2

2. (x + 2)(y - 6)

Apply FOIL: First: x * y = xy Outer: x * (-6) = -6x Inner: 2 * y = 2y Last: 2 * (-6) = -12

Combine the terms: Result: xy - 6x + 2y - 12

3. (4 - a)(5 - b)

Apply FOIL: First: 4 * 5 = 20 Outer: 4 * (-b) = -4b Inner: (-a) * 5 = -5a Last: (-a) * (-b) = ab

Combine the terms: Result: 20 - 4b - 5a + ab

4. (a - 2)(3 - a)

Apply FOIL: First: a * 3 = 3a Outer: a * (-a) = -a^2 Inner: (-2) * 3 = -6 Last: (-2) * (-a) = 2a

Combine the terms: Result: 3a - a^2 - 6 + 2a

Simplify: Result: 5a - a^2 - 6

5. (2x - 1)(3 + 4x)

Apply FOIL: First: 2x * 3 = 6x Outer: 2x * 4x = 8x^2 Inner: (-1) * 3 = -3 Last: (-1) * 4x = -4x

Combine the terms: Result: 6x + 8x^2 - 3 - 4x

Simplify: Result: 8x^2 + 2x - 3

Now let's simplify the given expressions:

1. 4x - (x - 1)(x + 3)

Distribute the negative sign inside the bracket: 4x - (x^2 + 3x - x - 3)

Combine like terms: 4x - (x^2 + 2x - 3)

Remove the parentheses and distribute the negative sign: 4x - x^2 - 2x + 3

Simplify: Result: -x^2 + 2x + 3

2. a² - (a + b)(a - 2b)

Distribute the negative sign inside the bracket: a² - (a² - 2ab + ab - 2b²)

Combine like terms: a² - (a² - ab - 2b²)

Remove the parentheses and distribute the negative sign: a² - a² + ab + 2b²

Simplify: Result: ab + 2b²

3. 20 + (4 - x)(x - 5)

Distribute 4 - x inside the bracket: 20 + (4x - 5x - x² + 5)

Combine like terms: 20 + (-x² - x + 9)

Simplify: Result: -x² - x + 29

4. (3x - 5)(x + 1) - 3x²

Apply FOIL: (3x * x) + (3x * 1) + (-5 * x) + (-5 * 1) - 3x²

Simplify: 3x² + 3x - 5x - 5 - 3x²

Combine like terms: 3x - 5

Result: 3x - 5

5. (-4x + 6)(-x - 2) - 4x²

Apply FOIL: (-4x * -x) + (-4x * -2) + (6 * -x) + (6 * -2) - 4x²

Simplify: 4x² + 8x - 6x - 12 - 4x²

Combine like terms: 8x - 6x - 12

Result: 2x - 12

Note: In expressions 4) and 5), the final results are simplified further after combining like terms.