A monomial is an algebraic expression which consists of one term only.
9x, 7a², -3mpx²
The number in front of the variables (letters) is called the coefficient. In the above 3 examples, 9, 7, and -3 are the coefficients.
Addition & Subtraction
In addition & subtraction, add or subtract the coefficients only and leave the variables intact (the same).
i) 15ab – 18ab = -3ab
ii) 3x + 2x – 7x = -2x
iii) -3y + 9y = 6y
iv) 17q + 9q – 4q – (-4q) = 26q – 4q + 4q = 26q
Multiplication of monomials
If 3.3 = 3² and y.y.y = y³, then a.a.a.b.b = a³b²
In multiplication, add the exponents of the same bases.
) = x3 + 5
ii) (x²y)(x³y²) = x2 + 3
y1 + 2
iii) (6k²)(15k³) = 90k2 + 3
n²) = [(-4)(3)](m2 + 4
)(n1 + 2
) = -12m6
v) (-7p²q)(-5pq²) = [(-7)(-5)](p2 + 1
)(q2 + 1
) = 35p³q³
vi) (3a²b³c)(-2b²c²d) = [(3)(-2)](a²)(b3 + 2
)(c1 + 2
)(d) = -6a²b5
In the above 4 examples, multiply the coefficients as well as add the exponents of the same bases.
When an algebraic term is being raised to a power, then multiply the exponents of each part of the term, (including the coefficient) by the power to which it is raised.
Multiply the exponents
[Multiply the exponents 3
[1 × 3 = 3, 3
v) (-5c²d³)³ = (-51
)³(c²)³(d³)³ = -125c6
Division of monomials
In the division, subtract the exponents of the denominator or divisor from the exponents of the numerator or dividend of the same base.
In examples (v) – (vii), divide the coefficients as well.
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