Question

2 parter part 1:

Answer 1

There are actually three ways to multiply binomials. I am not sure which ones you covered, so I will just mention the three:

A. Vertical method: Similar to multiplying whole numbers, you line up the given and multiply each term. The partial products should line up with similar terms before you add them together. 

B. Distributive: This method uses the distributive property of multiplication. Each term of each binomial will be distributed to the terms of the other. 

C. FOIL: Similar to the distributive method. FOIL is a mnemonic which means:

F = First term (Multiply the first terms of each binomial)
O = Outer terms (Multiply the terms that are on the outside)
I = Inner terms (Multiply the terms that are on the inside)
L = Last terms (Multiply the last terms of each binomial)

It is also important to note that the FOIL method works only on binomials. As for distributive and vertical, it can be used on polynomials. 

2. Using mnemonics are useful for memorizing. FOIL helps you remember the order in which you will multiply the terms. It is also less confusing than the distributive because it is a shorter process. 

3.
$(x+1)(x+3)$
$x(x+3)+1(x+3)$
$x^{2}+3x+1x+3$    Combine like terms
$x^{2}+4x+3$

4. 
$(y+6)(y+4)$
$y(y+4)+6(y+4)$
$y^{2}+4y+6y+24$ Combine like terms
$y^{2}+10y+24$

5. 
$(z-5)(z+3)$
$z(z+3)+(-5)(z+3)$ Remember to carry the sign
$z^{2}+3+(-5z)-15$ Combine like terms
$z^{2}-2z-15$

6.
$(a+8)(a-3)$
$a(a-3)+8(a-3)$   
$a^{2}-3a+8a-24)$ Combine like terms
$a^{2}+5a-24)$

7. 
$(g-7)(g-2)$
$g(g-2)+(-7)(g-2)$ Remember to carry the sign
$g^{2}-2g+(-7g)+14$ Combine like terms
$g^{2}-9g+14$

8. 
$(n-6)(n-4)$
$n(n-4)+(-6)(n-4)$  Remember to carry the sign
$n^{2}-4n+(-6n)+24$ Combine like terms
$n^{2}-10n+24$

9. 
$(3m+1)(m+9)$
$3m(m+9)+1(m+9)$ 
$3m^{2}+27m+m+9$ Combine like terms
$3m^{2}+28m+9$

10. 
$(2p-4)(3p+2)$
$2p(3p+2)+(-4)(3p+2)$
$6p^2+4p+(-12p)-8$ Combine like terms
$6p^2-8p-8$

11: 
$(6-5s)(2-s)$
$6(2-s)+(-5s)(2-s)$
$12-6s+(-10s)+5s^{2}$ Combine like terms
$12-16s+5s^{2}$ Arrange the terms in descending order and carry the signs.
$5s^{2}-16s+12$ 

13: (b+3) (b+7)
F = (b)(b) = b²
O= (b)(7) = 7b  
I = (3)(b) =3b
L = (3)(7) =21

b²+7b+3b+21
b²+10b+21

14: (w+9) (w+6)
F = (w)(w) = w²
O= (w)(6) = 6w  
I = (9)(w) =9w
L = (9)(6) =54
w²+6w+9w+54
w²+15w+54