Sure, let's analyze and simplify each given expression step-by-step.
### Expression e:
[tex]\[ 2ab + 5b + 10c + 4ac \][/tex]
This expression doesn't require any further simplification or factorization, as it is already in its simplest form.
### Expression f:
[tex]\[ 2y^3 - 36 - 6y^2 + 12y \][/tex]
Rearrange the terms to combine like terms:
[tex]\[ 2y^3 - 6y^2 + 12y - 36 \][/tex]
### Expression g:
[tex]\[ 6ab^2 + 5ab + b^2 + 30a^2b \][/tex]
This expression is also already in its simplest form. We list the terms by their degree and variable arrangement to see that no further simplification is necessary.
### Expression h:
[tex]\[ p(p + q - r) - qr \][/tex]
Distribute [tex]\( p \)[/tex] across the terms inside the parenthesis:
[tex]\[ p^2 + pq - pr - qr \][/tex]
The simplified form is:
[tex]\[ p(p + q - r) - qr \][/tex]
### Expression i:
[tex]\[ 2(2a + 5b) - 6ab - 15b^2 \][/tex]
Distribute the 2 inside the parenthesis:
[tex]\[ 4a + 10b - 6ab - 15b^2 \][/tex]
### Expression j:
[tex]\[ 15x^3yz + 5xy z - 3x^2 - 1 \][/tex]
This expression doesn't require further simplification as it is also already in its simplest form.
Combining all the simplified results, we have:
[tex]\[
(2ab + 4ac + 5b + 10c, \ 2y^3 - 6y^2 + 12y - 36, \ 30a^2b + 6ab^2 + 5ab + b^2, \ p(p + q - r) - qr, \ 4a - 6ab - 15b^2 + 10b, \ 15x^3 yz - 3x^2 + 5xy z - 1)
\][/tex]
And that matches the given expressions you provided.
