Factorise x squared + 4x + 3

 (x+1)(x+3)

Explanation:

Let's assume it factors into (x+a)(x+b)

The goal is to find the two numbers a and b.

FOIL out (x+a)(x+b) to get x^2+(a+b)x+ab

Note how a+b is the middle term and ab is the last term.

In the original expression, 4 is the middle term and 3 is the last term.

So we need to find two numbers that

add to 4multiply to 3

There are two ways to multiply to 3 and they are

1 times 3 = 3-1 times -3 = -3

But only the first way has the factors add to 4. So that means a = 1 and b = 3.

Therefore (x+a)(x+b) = (x+1)(x+3)

And x^2+4x+3 = (x+1)(x+3)

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)

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