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Nat2105 [25]
3 years ago
9

Problem type join results unknown

Mathematics
1 answer:
Allisa [31]3 years ago
8 0

<u>Not sure what you are asking for, but,</u>

<u>Here is an example of a JRU (Join Result Unknown)  word problem</u>:

There were _____ kids on the playground. ____ more kids came onto the playground. How many kids are on the playground?

<u>Here is an example of a JCU (Join Change Unknown)  word problem:</u>

There were ____ kids on the playground. Some more kids came on the playground. Now there are ____ kids on the playground. How many kids came on the playground?

<u> Here is an example of a JSU (Join Start Unknown)  word problem:</u>

Some kids were on the playground. ____ kids came on the playground. Now there are ____ kids on the playground. How many kids were on the playground at the beginning?



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Answer:

<u>Part 1</u>

Set B

<u>Part 2</u>

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

<u>Part 3</u>

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}

<u>Part 4</u>

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}

<u>Part 5</u>

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.

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