Question

Expressions is equivalent to a(b-c)-b(a+c)-c(a-b)?

Answer 1

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Answer 2

After solving the algebraic expression a(b-c)-b(a+c)-c(a-b) we get the equivalent answer as  ₋2(ab ₊ ac).

What is equivalent of algebraic expression?

Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given the expression is a(b₋c)₋b(a₊c)₋c(a₋b)

The first step is to multiply the terms.

⇒(a×b ₋ a×c) ₋ (b×a ₊ b×c) ₋ (c×a - c×b)

= (ab ₋ ac) ₋ (ba ₊ bc) ₋ (ca ₋ cb)

Now open the brackets.

= ab ₋ ac ₋ ba ₋ bc ₋ ca ₊ cb

Now comes main step of combining the like terms.

Put similar terms together on both sides of the equation.The two phrases are equal if each of the terms in both of them is the equivalent.

= ab ₋ ba ₋ ac ₋ ca ₋ bc ₊bc

Since, bc is a  like term with opposite sign, therefore bc  gets cancelled.

= ab ₋ ba ₋ ac ₋ ca

= ₋2ab ₋ 2ac

Take 2 as a common term from both the terms.

= ₋2(ab ₊ ac)

Hence we get the required equivalent of a(b-c)-b(a+c)-c(a-b) as

₋2(ab ₊ ac)

Learn more about "equivalent expressions" here-

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