Question

A) b(5-b)+2(5-b) б) 8(y+5)-(y+5)²

Answer 1

A: b(5-b)+2(5-b)=(b+2)•(5-b)
B: 8(y+5)-(y+5)(y+5)=(y+b)•(3-y)

Answer 2

Simplifying the Algebraic Expressions

To answer your question, let's simplify the given algebraic expressions step by step.

# A) Simplifying the expression b(5-b) + 2(5-b):

First, let's expand the brackets:

b(5-b) + 2(5-b) = 5b - b² + 10 - 2b

Now, let's combine like terms:

5b - b² + 10 - 2b = (5b - 2b) + (-b² + 10) = 3b - b² + 10

Therefore, the simplified expression is 3b - b² + 10.

# B) Simplifying the expression 8(y+5) - (y+5)²:

Let's simplify this expression step by step:

First, let's expand the brackets:

8(y+5) - (y+5)² = 8y + 40 - (y² + 10y + 25)

Next, let's simplify further by distributing the negative sign inside the second set of brackets:

8y + 40 - (y² + 10y + 25) = 8y + 40 - y² - 10y - 25

Now, let's combine like terms:

8y + 40 - y² - 10y - 25 = (8y - 10y) + (40 - 25) - y² = -2y + 15 - y²

Therefore, the simplified expression is -2y + 15 - y².

Summary:

To summarize, the given expressions have been simplified as follows:

A) The expression b(5-b) + 2(5-b) simplifies to 3b - b² + 10.

B) The expression 8(y+5) - (y+5)² simplifies to -2y + 15 - y².

Please let me know if you need any further assistance!