Question

A) Expand and simplify (4x + 3)(2x - 5)

Answer 1

Answer:

a. $8x^{2} -14x-15$

b. $(x+3)(x+2)$

Step-by-step explanation:

A. There are 3 methods (that I know of). The easiest method is the lattice multiplication, while the most commonly used is the FOIL method (First+Outer+Middle+Last)

For F, take the first terms of the 2 and multiply

$4x*2x=8x^{2}$

For O, take the outer terms and multiply

$4x*-5=-20x$

For I, take the inner terms and multiply

$3*2x=6x$

For L, take the last terms and multiply

$3*-5=-15$

After that, add all of them up

$8x^{2} +(-20x)+6x+(-15)=8x^{2}-14x-15$

B. Since the equation is in the form x^2+bx+c,

$(x+?)(x+?)$

Now we need to find 2 numbers that will add up to 5 and multiply to 6.

Here are some of the combinations of numbers that multiply to 6

3*2

1*6

-3*-2

-1*-6

3 and 2 add up to 5 so:

$(x+3)(x+2)$