Evan found a way to find the product of 36 x 15.

36 x 15 = ( 30 + 6 ) = ( 10 + 5 ) = 300 + 150 + 60 + 30 = 540

a. Does Evan's method work for finding 35 x 15? Explain.
b. Use Evan's method to find ( 2 + n )(3 + 5).
c. Use Evan's method to find ( n + 2)(a + 3).
d. Use Evan's method to find ( a + b)( c + d).

For A i think it works but i do not understand b,c, and d.

a. Evan's method does not work for finding 35 x 15. His method relies on breaking down one of the numbers into multiples of 10 and another number, which is possible for 36 x 15 because 36 can be broken down into 30 and 6. However, 35 cannot be easily broken down in the same way, making Evan's method ineffective in this case.

b. Using Evan's method, we can find ( 2 + n ) ( 3 + 5 ) as follows:
( 2 + n ) ( 3 + 5 ) = ( 2 + n ) ( 8 ) = 16 + 8n

c. Using Evan's method, we can find ( n + 2 ) ( a + 3 ) as follows:
( n + 2 ) ( a + 3 ) = ( n + 2 ) ( 3 + a ) = ( 3n + 6 ) + ( an + 2a ) = 3n + 6 + an + 2a

d. Using Evan's method, we can find ( a + b ) ( c + d ) as follows:
( a + b ) ( c + d ) = ( a + b ) ( d + c ) = ( ad + ac ) + ( bd + bc ) = ad + ac + bd + bc

a. Evan's method does not work for finding 35 x 15. Evan's method relies on splitting the numbers into their tens and units places and then multiplying those parts separately. However, the number 35 is not divisible into tens and units, so it cannot be split in the same way as 36.

b. To use Evan's method to find (2 + n)(3 + 5), we can distribute both terms within the parentheses to get:

(2 + n)(3 + 5) = 2(3 + 5) + n(3 + 5)

Now, we can split each term within the parentheses into its tens and units places:

= (2*3 + 2*5) + (n*3 + n*5)

Performing the calculations:

= (6 + 10) + (3n + 5n)
= 16 + 8n

So, (2 + n)(3 + 5) = 16 + 8n.

c. Similarly, to use Evan's method to find (n + 2)(a + 3), we distribute both terms within the parentheses:

(n + 2)(a + 3) = n(a + 3) + 2(a + 3)

Now, we can split each term within the parentheses into its tens and units places:

= (na + 3n) + (2a + 6)

Combining like terms:

= na + 3n + 2a + 6

So, (n + 2)(a + 3) = na + 3n + 2a + 6.

d. To use Evan's method to find (a + b)(c + d), we distribute both terms within the parentheses:

(a + b)(c + d) = a(c + d) + b(c + d)

Now, we can split each term within the parentheses into its tens and units places:

= (ac + ad) + (bc + bd)

Combining like terms:

= ac + ad + bc + bd

So, (a + b)(c + d) = ac + ad + bc + bd.