Question

1) (x²-x+4)(x-5); 3) (2-3a)(-a²+4a-8); 5) (x²-x+4)(2x²-x+4); 7) (8+4c)(2c²-c-4);​

Answer 1

Ответ:

1)x³-5x²-x²+5x+4x-20=x³-6x²+9x-20

3)-2a²+8a-16+3a³-12a²+24a=3a³-14a²+32a-16

5)2x⁴-x³+4x²-2x³+x²-4x+8x²-4x+16=2x⁴-3x³+13x²-8x+16

7)16c²-8c-32+8c³-4c²-16c=8c³-12c²-24c-32

Answer 2

It seems like you want to multiply the given binomial expressions. Let's multiply them step by step:

1. (x²-x+4)(x-5): To multiply these binomials, you can use the distributive property or the FOIL method (First, Outer, Inner, Last). Let's use the FOIL method:

(x² - x + 4)(x - 5) = x²(x) - x(x) + 4(x) - 5(x²) - 5(-x) - 5(4)

Now, simplify:

x³ - x² + 4x - 5x² + 5x - 20

Combine like terms:

x³ - 6x² + 9x - 20

So, (x²-x+4)(x-5) = x³ - 6x² + 9x - 20.

3. (2-3a)(-a²+4a-8): Let's use the FOIL method again:

(2 - 3a)(-a² + 4a - 8) = 2(-a²) + 2(4a) - 2(8) - 3a(-a²) - 3a(4a) - 3a(-8)

Now, simplify:

-2a² + 8a - 16 + 3a³ - 12a² + 24a

Combine like terms:

3a³ - 14a² + 32a - 16

So, (2-3a)(-a²+4a-8) = 3a³ - 14a² + 32a - 16.

5. (x²-x+4)(2x²-x+4): FOIL method:

(x² - x + 4)(2x² - x + 4) = x²(2x²) - x(2x²) + 4(2x²) + x²(-x) - x(-x) + 4(-x) + x²(4) - x(4) + 4(4)

Simplify:

2x⁴ - 2x³ + 8x² - x³ + x² - 4x + 4x² - 4x + 16

Combine like terms:

2x⁴ - 3x³ + 13x² - 8x + 16

So, (x²-x+4)(2x²-x+4) = 2x⁴ - 3x³ + 13x² - 8x + 16.

7. (8+4c)(2c²-c-4): FOIL method:

(8 + 4c)(2c² - c - 4) = 8(2c²) + 8(-c) + 8(-4) + 4c(2c²) + 4c(-c) + 4c(-4)

Simplify:

16c² - 8c - 32 + 8c³ - 4c² - 16c

Combine like terms:

8c³ + 12c² - 24c - 32

So, (8+4c)(2c²-c-4) = 8c³ + 12c² - 24c - 32.