Factorise the quadratic expression below: 𝑥2+8𝑥+7x 2 +8x+7

Sure, here is the step-by-step solution to factorize the quadratic expression x^2 + 8x + 7:

Step 1: Identify the coefficients of the quadratic expression. Here, a = 1 (coefficient of x^2), b = 8 (coefficient of x), and c = 7 (constant term).

Step 2: We need to find two numbers that multiply to give ac (ac = 17 = 7) and add up to give b (b = 8). The numbers are 7 and 1 because 7*1 = 7 and 7+1 = 8.

Step 3: Rewrite the middle term of the quadratic expression as the sum of the terms 7x and 1x. So, x^2 + 8x + 7 becomes x^2 + 7x + x + 7.

Step 4: Factor by grouping. The first two terms can be grouped together, and the last two terms can be grouped together. This gives us x(x + 7) + 1(x + 7).

Step 5: Notice that (x + 7) is a common factor. So, the expression can be written as (x + 7)(x + 1).

So, the factorized form of the quadratic expression x^2 + 8x + 7 is (x + 7)(x + 1).