Question

1) (x - 4)^2 - (x + 1)(x + 2) (x + 5)^2- 5x(2 – x) 16y + 2(y – 4 )^2 2) 9y^2 – 25 4a - a^3 -5a^2- 10ab - 5b^2 3) (6x -x^2)^2 -x^2 (x – 3)(x + 3) + 6x(3 +2x^2)

Answer 1

Объяснение:

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Answer 2

Let's simplify each of the given expressions:

a) (x - 4)^2 - (x + 1)(x + 2)

To simplify this expression, first expand the square and then distribute the terms:

(x - 4)^2 = x^2 - 8x + 16

Now, distribute (x + 1)(x + 2):

(x + 1)(x + 2) = x^2 + 2x + x + 2 = x^2 + 3x + 2

Now, subtract the second expression from the first:

(x^2 - 8x + 16) - (x^2 + 3x + 2)

Now, subtract each term:

x^2 - 8x + 16 - x^2 - 3x - 2

Now, combine like terms:

(-8x - 3x) + (16 - 2) = -11x + 14

So, the simplified expression is: -11x + 14

b) (x + 5)^2 - 5x(2 - x)

Expand (x + 5)^2:

(x + 5)^2 = x^2 + 10x + 25

Now, distribute the terms:

x^2 + 10x + 25 - 5x(2 - x)

Distribute the -5x:

x^2 + 10x + 25 - 10x + 5x^2

Now, combine like terms:

(x^2 + 5x^2) + (10x - 10x) + 25

6x^2 + 25

So, the simplified expression is: 6x^2 + 25

c) 16y + 2(y - 4)^2

Expand (y - 4)^2:

(y - 4)^2 = y^2 - 8y + 16

Now, distribute the terms:

16y + 2(y^2 - 8y + 16)

Distribute the 2:

16y + 2y^2 - 16y + 32

Now, combine like terms:

(16y - 16y) + (2y^2 + 32)

The 16y terms cancel out:

2y^2 + 32

So, the simplified expression is: 2y^2 + 32

a) 9y^2 - 25

This expression is already simplified, and it represents the difference of squares:

9y^2 - 25 = (3y)^2 - 5^2 = (3y - 5)(3y + 5)

So, the simplified expression is: (3y - 5)(3y + 5)

b) 4a - a^3 - 5a^2 - 10ab - 5b^2

This expression doesn't have any common factors to simplify further, so it remains as it is:

4a - a^3 - 5a^2 - 10ab - 5b^2

(6x - x^2)^2 - x^2 (x - 3)(x + 3) + 6x(3 + 2x^2)

First, expand (6x - x^2)^2:

(6x - x^2)^2 = (6x - x^2)(6x - x^2)

Now, use FOIL (First, Outer, Inner, Last) to expand it:

(6x - x^2)(6x - x^2) = 36x^2 - 6x^3 - 6x^3 + x^4

Combine like terms:

x^4 - 12x^3 + 36x^2

Now, expand (x - 3)(x + 3):

(x - 3)(x + 3) = x^2 - 9

Now, we can rewrite the expression:

(x^4 - 12x^3 + 36x^2) - x^2(x^2 - 9) + 6x(3 + 2x^2)

Distribute x^2 in the second term:

x^4 - 12x^3 + 36x^2 - (x^4 - 9x^2) + 6x(3 + 2x^2)

Now, simplify:

x^4 - 12x^3 + 36x^2 - x^4 + 9x^2 + 18x + 12x^3

Now, combine like terms:

(36x^2 + 9x^2) - 12x^3 + 12x^3 + 18x

45x^2 + 18x

So, the simplified expression is: 45x^2 + 18x