Expand the expression and combine the like terms:
\large{expr(["+", ["*", A, X], ["*", F, ["+", ["*", B, X], D]]])}
The minus sign in front of the parentheses means we
multiply each term inside the parentheses by
\purple{F}:
Distribute the \purple{F} into the parentheses:
\qquad expr(["*", A, X])
F < 0 ? "" : "+"
\purple{F(}\gray{expr(["+", ["*", B, X], D])}\purple{)}
\qquad expr(["*", A, X])
(F * B) < 0 ? "" : "+"
\purple{expr(["+", ["*", F * B, X], F * D])}
Combine the X terms:
\qquad\pink{expr(["*", A, X]) + expr(["*", F * B, X])} + F * D
\qquad\pink{expr(["*", A + (F * B), X])} + F * D
The simplified expression is expr(["*", A + (F * B), X])
The simplified expression is expr(["+", ["*", A + (F * B), X], F * D])
\large{expr(["+", C, ["*", F, ["+", ["*", B, X], D]]])}
The minus sign in front of the parentheses means we
multiply each term inside the parentheses by
\purple{F}:
Distribute the \purple{F} into the parentheses:
\qquad C
F < 0 ? "" : "+"
\purple{F(}\gray{expr(["+", ["*", B, X], D])}\purple{)}
\qquad C
(F * B) < 0 ? "" : "+"
\purple{expr(["+", ["*", F * B, X], F * D])}
Rewrite the expression to group the numeric terms:
\qquad expr(["*", F * B, X])
C < 0 ? "" : "+"
\blue{C + F * D}
Combine the numeric terms:
\qquad expr(["*", F * B, X])
(C + F * D) < 0 ? "" : "+"
\blue{C + F * D}
The simplified expression is expr(["*", F * B, X])
The simplified expression is expr(["+", ["*", F * B, X], C + F * D])
\large{expr(["+", ["*", E, ["+", C, ["*", A, X]]], ["*", F, ["+", ["*", B, X], D]]])}
The minus sign in front of the parentheses means we
multiply each term inside the first parentheses by
\purple{E}:
Distribute the \purple{E} into the first set of parentheses:
\qquad
\purple{E(}\gray{expr(["+", C, ["*", A, X]])}\purple{)}
+ expr(["*", F, ["+", ["*", B, X], D]])
\qquad
\purple{expr(["+", E * C, ["*", E * A, X]])}
+ expr(["*", F, ["+", ["*", B, X], D]])
The minus sign in front of the parentheses means we
multiply each term inside the parentheses by
\purple{F}:
Distribute the \purple{F} into the parentheses:
\qquad expr(["+", E * C, ["*", E * A, X]])
F < 0 ? "" : "+"
\purple{F(}\gray{expr(["+", ["*", B, X], D])}\purple{)}
\qquad expr(["+", E * C, ["*", E * A, X]])
(F * B) < 0 ? "" : "+"
\purple{expr(["+", ["*", F * B, X], F * D])}
Rewrite the expression to group the
\pink{X} terms and
numeric terms:
\qquad\pink{expr(["*", E * A, X]) +
expr(["*", F * B, X])} (E * C) < 0 ? "" : "+"
\blue{E * C + F * D}
Combine the \pink{X} terms:
\qquad\pink{expr(["*", E * A + F * B, X])}
(E * C) < 0 ? "" : "+"
\blue{E * C + F * D}
Combine the numeric terms:
\qquad\pink{expr(["*", E * A + F * B, X])}
(E * C + F * D) < 0 ? "" : "+"
\blue{E * C + F * D}
The simplified expression is expr(["*", E * A + F * B, X])
The simplified expression is expr(["+", ["*", E * A + F * B, X], E * C + F * D])
\large{expr(["+", ["*", E, ["+", ["*", A, X], C]], ["*", F, ["+", D, ["*", B, X]]]])}
The minus sign in front of the parentheses means we
multiply each term inside the first parentheses by
\purple{E}:
Distribute the \purple{E} into the first set of parentheses:
\qquad
\purple{E(}\gray{expr(["+", ["*", A, X], C])}\purple{)}
+ expr(["*", F, ["+", D, ["*", B, X]]])
\qquad
\purple{expr(["+", ["*", E * A, X], E * C])}
+ expr(["*", F, ["+", D, ["*", B, X]]])
The minus sign in front of the parentheses means we
multiply each term inside the parentheses by
\purple{F}:
Distribute the \purple{F} into the parentheses:
\qquad expr(["+", ["*", E * A, X], E * C])
F < 0 ? "" : "+"
\purple{F(}\gray{expr(["+", D, ["*", B, X]])}\purple{)}
\qquad expr(["+", ["*", E * A, X], E * C])
(F * D) < 0 ? "" : "+"
\purple{expr(["+", F * D, ["*", F * B, X]])}
Rewrite the expression to group the
\pink{X} terms and
numeric terms:
\qquad\pink{expr(["*", E * A, X]) +
expr(["*", F * B, X])} (E * C) < 0 ? "" : "+"
\blue{E * C + F * D}
Combine the \pink{X} terms:
\qquad\pink{expr(["*", E * A + F * B, X])}
(E * C) < 0 ? "" : "+"
\blue{E * C + F * D}
Combine the numeric terms:
\qquad\pink{expr(["*", E * A + F * B, X])}
(E * C + F * D) < 0 ? "" : "+"
\blue{E * C + F * D}
The simplified expression is expr(["*", E * A + F * B, X])
The simplified expression is expr(["+", ["*", E * A + F * B, X], E * C + F * D])