Equivalent Expressions: ""The area (in square meters), a, of a yard is given by...."
Hi, first post, and probably not my last lol
Ive been using Kahn Academy to teach myself maths again from the begining. One of the frustrating things about that site is sometimes they start throwing questions at you that none of their videos seemed to have covered, atleast not fully. Leaving me to scratch my head a bit.
One such question is:
"The area (in square meters), a, of a yard is given by the expression:
a=x^4+18x^2+81
Where X is a positive integer and each dimension is greater than 1 meter. What are two (not necessarily unique) expressions that could represent the dimensions of the yard ?
In the answer box, write these two expressions as a product that equals the area (e.g. "(expression 1)(expression 2)")."
The answer and "working out" are:
step 1: x^4+18x^2+81 = (x^2 + 9)^2
Step 2: (X^2+9)(X^2+9)
I understand how to go from step 1 to step 2. But what I can't figure out is how they got step 1. Theres no method shown, and all the videos leading up to this had no similar examples, and I understood them all up to that point.
What I understand is, they want an equivelant expression that is the product of two expressions.
I see the the 81 was made into 9^2 and the x^4 became (x^2)^2? but I can't seem to figure where does the 18x^2 fit into this?
thanks for any help. Also more resources that cover this would be good if you know any.
I don't like to move on until i understand this fully
Hi, first post, and probably not my last lol
Ive been using Kahn Academy to teach myself maths again from the begining. One of the frustrating things about that site is sometimes they start throwing questions at you that none of their videos seemed to have covered, atleast not fully. Leaving me to scratch my head a bit.
One such question is:
"The area (in square meters), a, of a yard is given by the expression:
a=x^4+18x^2+81
Where X is a positive integer and each dimension is greater than 1 meter. What are two (not necessarily unique) expressions that could represent the dimensions of the yard ?
In the answer box, write these two expressions as a product that equals the area (e.g. "(expression 1)(expression 2)")."
The answer and "working out" are:
step 1: x^4+18x^2+81 = (x^2 + 9)^2
Step 2: (X^2+9)(X^2+9)
I understand how to go from step 1 to step 2. But what I can't figure out is how they got step 1. Theres no method shown, and all the videos leading up to this had no similar examples, and I understood them all up to that point.
What I understand is, they want an equivelant expression that is the product of two expressions.
I see the the 81 was made into 9^2 and the x^4 became (x^2)^2? but I can't seem to figure where does the 18x^2 fit into this?
thanks for any help. Also more resources that cover this would be good if you know any.
I don't like to move on until i understand this fully
Last edited: