Question

1. $\begin{bmatrix} 1&-1\\ -4&-2end{bmatrix} +\begin{bmatrix} 5&-1\\ 3&0end{bmatrix}$
2. factor a difference of squares

$4x^{2}-25$

1. factor the trinomial

$x^{2}+7x+10$

Explanation:

Step1: Add corresponding matrix elements

$$\begin{bmatrix} 1+5 & -1+(-1) \\ -4+3 & -2+0 \end{bmatrix} = \begin{bmatrix} 6 & -2 \\ -1 & -2 \end{bmatrix}$$

Step2: Rewrite as difference of squares

$4x^2-25=(2x)^2-5^2$

Step3: Apply difference of squares rule

$(2x)^2-5^2=(2x-5)(2x+5)$

Step4: Find factors for trinomial

Find two numbers: $2+5=7$, $2\times5=10$

Step5: Factor the trinomial

$x^2+7x+10=(x+2)(x+5)$

Answer:

4)

$$\begin{bmatrix} 6 & -2 \\ -1 & -2 \end{bmatrix}$$

1. $(2x-5)(2x+5)$
2. $(x+2)(x+5)$