Question

1. $x^2 + 7xy + 6y^2$

Explanation:

Step1: Factor the quadratic

We need to factor \(x^{2}+7xy + 6y^{2}\). We look for two numbers that multiply to \(6\) (the coefficient of \(y^{2}\)) and add up to \(7\) (the coefficient of \(xy\)). The numbers are \(1\) and \(6\).

Step2: Write the factored form

Using the numbers \(1\) and \(6\), we can factor the quadratic as \((x + y)(x+6y)\). To check using the box method (area model), the first term \(x^{2}\) comes from \(x\times x\), the last term \(6y^{2}\) comes from \(y\times6y\), and the middle term \(7xy\) comes from \(x\times6y+x\times y=6xy + xy = 7xy\). So the factors are \((x + y)\) and \((x + 6y)\).

Answer:

The factored form of \(x^{2}+7xy + 6y^{2}\) is \((x + y)(x + 6y)\)