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Student Question

Secondary IV • 5mo.

Hi!

I'm currently learning about trinomial factoring, and I understand it pretty well, but there are a few questions that are giving me a tough time.

For example: 16y^2+56y+49

Here's another one: 15x^2+12+29x

It's usually the questions where when a and c get multiplied and a big number produces that give me trouble. I know that a x c = m x n, but in the first example, when I multiply 49 and 16 and get 784, I can't find the two numbers (m and n) that equal that when multiplied and then get 56 when added.

Am I doing something wrong? If I could have a step by step solution on how to answer a question like that I'd very much appreciate it. I hope my question makes sense.

Mathematics

Explanations (2)

• Explanation from Alloprof

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

Options
Team Alloprof • 5mo.

Hi !

There are different methods for factoring thes expressions :

There is such a number. For exemple, you can try 28 this way :

$$16y^2+56y+49$$

$$16y^2+28y+28y+49$$

You should try first two numbers that add up to 56, then try the product. Unfortunately, it might be more of a trial and error situation.

If you have any other questions, feel free to ask them !

• Options
5mo. edited September 2023

For the first example no need to search a, b,c m,n

just take a look

16y^2+56y+49 16=4^2 49=7^2

(4y)^2+56y+7^2

(4y)^2+2 4y 7+7^2

it seams like (a+b)^2=a^2+2ab+b^2

(4y)^2+2 4y 7+7^2=(4y+9)^2

befor doing any operation try to find if it is one of thes cases

(a+b)^2=a^2+2ab+b^2

(a-b)^2=a^2-2ab+b^2

a^2-b^2=(a+b)(a-b)