Question

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answer 1

Answer:

Part 1

Set B

Part 2

We can use the FOIL method to multiply these expressions:

$\textsf{FOIL}: \quad(a+b)(c+d)=ac+ad+bc+bd$

However, as all the expression are in the format $(a+b)^2$, we can use the shortcut:  $(a+b)^2=a^2+2ab+b^2$

Part 3

Using the shortcut to find the products:

$\begin{aligned}\implies (x+5)(x+5)& =(x+5)^2\\ & =x^2+2(x)(5)+5^2\\ & =x^2+10x+25\end{aligned}$

$\begin{aligned}\implies (2x+9)(2x+9) & = (2x+9)^2\\ & = (2x)^2+2(2x)(9)+9^2\\ & = 4x^2+36x+81\end{aligned}$

$\begin{aligned}\implies (x+1)^2 & = x^2+2(x)(1)+1^2\\ & = x^2+2x+1\end{aligned}$

Part 4

A new example of a multiplication problem based on the structure of Set B is:  $(3x+2)(3x+2)$

$\begin{aligned}\implies (3x+2)(3x+2) & = (3x+2)^2\\ & = (3x)^2+2(3x)(2)+2^2\\ & = 9x^2+12x+4\end{aligned}$

Part 5

An example of a multiplication problem that would NOT be included in Set B based on its structure is: $(x+2)(x-2)$

We cannot use the derived Set B shortcut (from part 2) to multiply this expression.  Instead, we would have to use a different shortcut of "The Difference of Two Squares" to find the product of this example expression.