Reading Blueprints. Find a polynomial that represents a. the difference in the length and width

Reading Blueprints. Find a polynomial that represents a. the...

Key Concepts

Blueprint Reading

Blueprint reading is the process of interpreting technical drawing details such as dimensions, scales, and geometric relationships. It often involves applying algebraic techniques to convert physical measurements into mathematical expressions like polynomials, aiding in precise construction and planning.

Polynomial

A polynomial is an algebraic expression involving a sum of powers in one or more variables multiplied by coefficients. It is used to model relationships and quantities in various contexts, including geometry and blueprint measurements.

Difference Expression

A difference expression involves subtracting one term from another to represent the change or disparity between two quantities. In the context of dimensions from a blueprint, it is used to express the difference between the length and width of a room.

Perimeter Calculation

Perimeter refers to the total distance around a geometric shape, typically calculated by adding together the lengths of all sides. Representing the perimeter as a polynomial involves creating an algebraic expression that combines the dimensions of the shape in a systematic way.

Transcript

00:01 So in this problem, we're given the blueprint of a house, which i drew a little bit of onto the right.

00:07 I didn't put in all of the different rooms.

00:09 I only put in the bedroom because reading the problem, that's the only specific room that we're going to be talking about.

00:14 But i did put in all of the other measurements.

00:17 So in part a, they're being asked to find the difference in the length versus the width of that one bedroom.

00:23 Remember, difference means subtraction.

00:26 So they want us to subtract the length from the width.

00:30 So if we want to find the difference in the length, in the length, and the width.

00:47 So in our bedroom, the length of it is 4x plus 3, and the width of the bedroom is x squared minus 6x plus 3.

00:55 So if we want to find the difference between the length and the width, we simply need to subtract them.

01:01 Well, our width is the quantity, x squared, minus 6x plus 3, minus the length, which is 4x plus 3.

01:11 Well, essentially, we're just subtracting polynomials.

01:15 So the terms in the first polynomial will just get brought down.

01:18 So we'll have x squared minus 6x plus 3.

01:23 And for the second polynomial, we simply need to change their signs.

01:26 So the positive 4x becomes negative 4x, and the positive 3 becomes negative 3.

01:31 And now we simply need to combine light terms.

01:34 Well, you notice the x squared does not have a light term, so that will get brought down.

01:39 Negative 6x has a late term of negative 4x, well negative 6x minus 4x is negative 10x, and positive 3 has a late term of negative 3, but those are going to cancel each other out.

01:52 So what we find is the difference between the length and the width is the quantity x squared minus 10x.

01:59 Because our problem gives us units, we should use those in our final answer.

02:02 So she also mentioned that it's difference in fee.

02:07 Now for part b, we're being asked to find the perimeter of the entire apartment.

02:13 Well, to find perimeter, we essentially just need to add up all the side lengths.

02:17 Well, because it's a rectangle, the width is going to be the same on both sides, and the length will also be the same on both sides.

02:26 So for part b, to find the perimeter, essentially we can do two times what we would get when we do the width plus two times the length.

02:36 Well, to find the width, we need to add 3x plus 1 and x squared minus 6x plus 3.

02:42 So we're going to do 2 times the quantity of 3x plus 1 plus the quantity of x squared minus 6x plus 3.

02:55 And then we're going to add this to 2 times our length.

02:59 Well, our length, we need to add x squared minus x plus 6 plus 4x plus 3.

03:04 So we'll have plus two times the quantity of x squared minus x plus six plus the quantity of 4x plus three.

03:16 So now looking within that first set of parentheses, because we're adding, we simply need to combine like terms.

03:22 So we will be left with two times the quantity of.

03:26 Now let's find our light terms.

03:28 Let's start with our x squared term.

03:29 It doesn't have a like term, so we just need to bring it down.

03:33 Our next term is 3x, which light term is negative 6...

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