Match Equivalent Expressions: (2a+b)(b+4) and Related Polynomials

Join expressions of equal value

1. $(2a+b)(b+4)$

2. $(4+a)(2b+b)$

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

4. $(2a-b)(b+4)$

   a.$2ab-8a-b^2+4b$

   b.$12b+3ab$

   c.$2ab+8a-b^2-4b$

   d.$2ab+8a+b^2+4b$

To solve this problem, we need to expand each given expression and compare it to the list of provided expanded expressions.

Let's expand each of the four expressions:

• Expression 1: $(2a+b)(b+4)$

Applying the distributive property:

$(2a+b)(b) + (2a+b)(4) = 2ab + b^2 + 8a + 4b$ This matches the expanded form $2ab + b^2 + 8a + 4b$, option d.
• Expression 2: $(4+a)(2b+b) = (4+a)(3b)$

Distributing the terms:

$3b \cdot 4 + 3b \cdot a = 12b + 3ab$ This matches the expanded form $12b + 3ab$, option b.
• Expression 3: $(2a-b)(b-4)$

Distributing the terms:

$2a \cdot b - 2a \cdot 4 - b \cdot b + b \cdot 4 = 2ab - 8a - b^2 + 4b$ This matches the expanded form $2ab - 8a - b^2 + 4b$, option a.
• Expression 4: $(2a-b)(b+4)$

Distributing the terms:

$2a \cdot b + 2a \cdot 4 - b \cdot b - b \cdot 4 = 2ab + 8a - b^2 - 4b$ This matches the expanded form $2ab + 8a - b^2 - 4b$, option c.

Therefore, the correct matching is as follows:

• Expression 1: $(2a+b)(b+4)$ matches with $2ab+8a+b^2+4b$
• Expression 2: $(4+a)(2b+b)$ matches with $12b+3ab$
• Expression 3: $(2a-b)(b-4)$ matches with $2ab-8a-b^2+4b$
• Expression 4: $(2a-b)(b+4)$ matches with $2ab+8a-b^2-4b$

Thus, the correct answer is: 1-d, 2-b, 3-a, 4-c.