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Algebraic expressions

Lessons 2 · 1 lessons · Sh.A. Alimov, A.R. Xalmukhamedov, M.A. Mirzaakhmedov. Algebra: textbook for Grade 8 of general secondary schools. Revised 4th edition. Tashkent: “O‘qituvchi”, 2019
2

Algebraic expressions

Textbook: pp. 7–11
GoalKnow what an algebraic expression, its numerical value and an integral expression are; reduce an integral expression to a standard polynomial.
New words
algebraic expression · algebraik ifodanumerical value of an expression · ifodaning son qiymatiintegral expression · butun ifodastandard polynomial · standart ko‘phad
Explanation

A record made of numbers and letters joined by operation signs is called an algebraic expression. If we put numbers in place of the letters and carry out the operations, we get the numerical value of the expression. For example, in 3a + 2b - 7 with a = 2 and b = 3 the value is 3 · 2 + 2 · 3 - 7 = 5. An expression built from polynomials using only addition, subtraction and multiplication is called an integral expression. Any integral expression can be reduced to a standard polynomial by opening brackets and collecting like terms. Algebraic expressions let us translate a problem into mathematical language, where a letter stands for any number.

Worked examples
The value of 2x² - 3x + 4 at x = -1: 2 · (-1)² - 3 · (-1) + 4 = 2 + 3 + 4 = 9.
Reduce the integral expression to a standard polynomial: (a + 2b)(a - b) - a(a + b) = a² + ab - 2b² - a² - ab = -2b².
Class activity

“Mystery number”: each pupil thinks of a number and follows the teacher’s steps (multiply by 2, add 8, divide by 2, subtract the number). Everyone gets 4, and the class proves it with a letter.

Practice
1
Find the value of 3a - 2b for a = 4, b = 5.
2
Write the sum of two consecutive natural numbers, the smaller being n, as an expression and simplify it.
3
A notebook costs 3000 so‘m and a pen 1500 so‘m. The cost of d notebooks and q pens is p = 3000d + 1500q. Find p for d = 5, q = 4.
4
Why does the value of 2(a + 3) - 2a not depend on a?