Question

1) (x+8) (x-5)-x в квадрате +7x2) (2y-1) (y+8)3) (2a-1) (a+5)-a(a-3)4) (a+4) (a+5 (a+2)

Answer 1

1) x2-5x+8x-40-x2+7x=10x-40=10(x-4)

2) 2y2+16y-y-8=2y2+15y-8

3)2a2+10a-a-5=2a2+9a-5

4)a2+5a+4a+20(a+2) =a3+2a2+9a2+18a+20a+40=a3+11a2+38a+40

Answer 2

To simplify the given expressions, let's expand them step by step:

1. (x+8) (x-5) - x^2 + 7x^2 Expand the first part: (x+8) (x-5) = x(x) + x(-5) + 8(x) + 8(-5) = x^2 - 5x + 8x - 40 = x^2 + 3x - 40

Now, the expression becomes: x^2 + 3x - 40 - x^2 + 7x^2

Combine the like terms: 7x^2 - x^2 + 3x - 40 = 6x^2 + 3x - 40

2. (2y-1) (y+8) Expand the expression: (2y-1) (y+8) = 2y(y) + 2y(8) - 1(y) - 1(8) = 2y^2 + 16y - y - 8 = 2y^2 + 15y - 8

3. (2a-1) (a+5) - a(a-3) Expand the first part: (2a-1) (a+5) = 2a(a) + 2a(5) - 1(a) - 1(5) = 2a^2 + 10a - a - 5 = 2a^2 + 9a - 5

Now, the expression becomes: 2a^2 + 9a - 5 - a(a-3)

Distribute the 'a' in the second term: 2a^2 + 9a - 5 - (a^2 - 3a)

Remove the parentheses and combine like terms: 2a^2 + 9a - 5 - a^2 + 3a = 2a^2 - a^2 + 9a + 3a - 5 = a^2 + 12a - 5

4. (a+4) (a+5) (a+2) Expand the expression: (a+4) (a+5) (a+2) = (a+4) [(a+5) (a+2)]

Now, expand the inner part: (a+5) (a+2) = a(a) + a(2) + 5(a) + 5(2) = a^2 + 2a + 5a + 10 = a^2 + 7a + 10

Now, the expression becomes: (a+4) (a^2 + 7a + 10)

Distribute the 'a+4': (a+4) (a^2 + 7a + 10) = a(a^2) + a(7a) + a(10) + 4(a^2) + 4(7a) + 4(10) = a^3 + 7a^2 + 10a + 4a^2 + 28a + 40 = a^3 + 11a^2 + 38a + 40

So, the simplified expressions are:

1. 6x^2 + 3x - 40
2. 2y^2 + 15y - 8
3. a^2 + 12a - 5
4. a^3 + 11a^2 + 38a + 40