Simplify: A(B − C) + B(C − A) + C(A − B) - Mathematics

Simplify: a(b − c) + b(c − a) + c(a − b)

Answer in Brief

To simplify, we will use distributive law as follows:

\[a\left( b - c \right) + b\left( c - a \right) + c\left( a - b \right)\]

\[ = ab - ac + bc - ba + ca - cb \]

\[ = ab - ba - ac + ca + bc - cb\]

\[ = 0\]

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Chapter 6: Algebraic Expressions and Identities - Exercise 6.4 [Page 21]

Chapter 6 Algebraic Expressions and Identities
Exercise 6.4 | Q 20.06 | Page 21

Find each of the following product:
(−5a) × (−10a²) × (−2a³)

Express each of the following product as a monomials and verify the result in each case for x = 1:
(3x) × (4x) × (−5x)

Find the value of (5x⁶) × (−1.5x²y³) × (−12xy²) when x = 1, y = 0.5.

Find the following product:
0.1y(0.1x⁵ + 0.1y)

Find the following product:
1.5x(10x²y − 100xy²)

Simplify: x²(x² + 1) − x³(x + 1) − x(x³ − x)

Multiply:
(x² + y²) by (3a + 2b)

Multiply:
(2x² − 1) by (4x³ + 5x²)

Find the following product and verify the result for x = − 1, y = − 2:
(3x − 5y) (x + y)

Simplify : (x − y)(x + y) (x² + y²)(x⁴ + y²)