To find the expression for [tex]\( A - 3B \)[/tex] in standard form, we start by substituting the given expressions for [tex]\( A \)[/tex] and [tex]\( B \)[/tex].
Given:
[tex]\[ A = -2p + 7 \][/tex]
[tex]\[ B = p^2 + 3p - 5 \][/tex]
We need to find [tex]\( A - 3B \)[/tex].
First, we multiply [tex]\( B \)[/tex] by 3:
[tex]\[ 3B = 3(p^2 + 3p - 5) \][/tex]
[tex]\[ 3B = 3p^2 + 9p - 15 \][/tex]
Next, we subtract [tex]\( 3B \)[/tex] from [tex]\( A \)[/tex]:
[tex]\[ A - 3B = (-2p + 7) - (3p^2 + 9p - 15) \][/tex]
[tex]\[ A - 3B = -2p + 7 - 3p^2 - 9p + 15 \][/tex]
Now, we combine like terms:
[tex]\[ A - 3B = -3p^2 + (-2p - 9p) + (7 + 15) \][/tex]
[tex]\[ A - 3B = -3p^2 - 11p + 22 \][/tex]
So, the expression for [tex]\( A - 3B \)[/tex] in standard form is:
[tex]\[ \boxed{-3p^2 - 11p + 22} \][/tex]
