Procedure for find product of algebraic expression
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In multiplication of algebraic expression before taking up the product of algebraic expressions, let us look at two simple rules.
(i) The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
(ii) if x is a variable and m, n are positive integers, then
(xᵐ × xⁿ) = xm+nm+n
Thus, (x³ × x⁵) = x⁸, (x⁶ + x⁴) = x6+46+4 = x1010, etc.
I. Multiplication of Two Monomials
Rule:
Product of two monomials = (product of their numerical coefficients) × (product of their variable parts)
Find the product of: (i) 6xy and -3x²y³
Solution:
(6xy) × (-3x²y³)
= {6 × (-3)} × {xy × x²y³}
= -18x1+21+2 y1+31+3
= -18x³y⁴.
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