☰ Contents · Algebra

Multiplying monomials

Lessons 15 · 1 lessons · Sh.A. Alimov, O.R. Xolmuhamedov, M.A. Mirzaahmedov. Algebra, Grade 7, revised and expanded 5th edition. O‘qituvchi NMIU, Tashkent, 2017
15

Multiplying monomials

Textbook: pp. 72–74
GoalMultiply monomials and raise a monomial to a natural power.
New words
multiplying monomials · birhadlarni ko‘paytirishraising a monomial to a power · birhadni darajaga ko‘tarishproduct of coefficients · koeffitsiyentlar ko‘paytmasiletter part · harfiy qism
Explanation

When multiplying monomials we multiply the coefficients and combine equal letters by adding their exponents, according to the property of powers: (3a²b)(4ab³) = 12a³b⁴. The result is again a monomial and is written in standard form. When raising a monomial to a power, both the coefficient and every letter power are raised to that power, and the exponents are multiplied: (2x²y)³ = 2³ · (x²)³ · y³ = 8x⁶y³. With a negative coefficient we watch the sign: an even power gives a positive result. The power is done first, then the multiplication. The value of the resulting monomial is easy to find for given values of the letters.

Worked examples
(5a²b)(-2ab³) = (5 · (-2)) · (a² · a) · (b · b³) = -10a³b⁴.
(-3x²y)³ = (-3)³ · (x²)³ · y³ = -27x⁶y³; (-3x²y)² = 9x⁴y².
Class activity

“Monomial machine”: the class splits into two groups. One group names a monomial, the other raises it to a power or multiplies it by another monomial and checks the result on the board.

Practice
1
Multiply (5ab²)(-2a³b).
2
Raise (-3x²y)³ to the power.
3
Find the value of (2a)(3a²) at a = -2.
4
Why is 3a² · 4a³ equal to 12a⁵ and not 12a⁶?