a(b – c) (b + c) – d(c – b).
Answers
Answer:
(a-d)(b-c)(b+c)(c-b)
Step-by-step explanation:
1 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a
2
−b
2
=(a+b)(a−b).
(a-d)({b}^{2}-{c}^{2})(c-b)
(a−d)(b
2
−c
2
)(c−b)
2 Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd(a+b)(c+d)=ac+ad+bc+bd.
(a{b}^{2}-a{c}^{2}-d{b}^{2}+d{c}^{2})(c-b)
(ab
2
−ac
2
−db
2
+dc
2
)(c−b)
3 Expand by distributing sum groups.
a{b}^{2}(c-b)-a{c}^{2}(c-b)-d{b}^{2}(c-b)+d{c}^{2}(c-b)
ab
2
(c−b)−ac
2
(c−b)−db
2
(c−b)+dc
2
(c−b)
4 Expand by distributing terms.
a{b}^{2}c-a{b}^{3}-a{c}^{2}(c-b)-d{b}^{2}(c-b)+d{c}^{2}(c-b)
ab
2
c−ab
3
−ac
2
(c−b)−db
2
(c−b)+dc
2
(c−b)
5 Expand by distributing terms.
a{b}^{2}c-a{b}^{3}-(a{c}^{3}-a{c}^{2}b)-d{b}^{2}(c-b)+d{c}^{2}(c-b)
ab
2
c−ab
3
−(ac
3
−ac
2
b)−db
2
(c−b)+dc
2
(c−b)
6 Expand by distributing terms.
a{b}^{2}c-a{b}^{3}-(a{c}^{3}-a{c}^{2}b)-(d{b}^{2}c-d{b}^{3})+d{c}^{2}(c-b)
ab
2
c−ab
3
−(ac
3
−ac
2
b)−(db
2
c−db
3
)+dc
2
(c−b)
7 Expand by distributing terms.
a{b}^{2}c-a{b}^{3}-(a{c}^{3}-a{c}^{2}b)-(d{b}^{2}c-d{b}^{3})+d{c}^{3}-d{c}^{2}b
ab
2
c−ab
3
−(ac
3
−ac
2
b)−(db
2
c−db
3
)+dc
3
−dc
2
b
8 Remove parentheses.
a{b}^{2}c-a{b}^{3}-a{c}^{3}+a{c}^{2}b-d{b}^{2}c+d{b}^{3}+d{c}^{3}-d{c}^{2}b
ab
2
c−ab
3
−ac
3
+ac
2
b−db
2
c+db
3
+dc
3
−dc
2
b