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A short class with Sarah and her students. The other ways are under More.
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Here is our expression: 5x³ − 2x² + 7x − 4. How many terms can you find?
Four: 5x³, −2x², 7x and −4.
Why did you write −2x² with a minus sign?
Because the sign in front of a term belongs to it. So the coefficient of x² is −2, not 2.
Exactly. And which term has no variable?
−4. It is the constant term.
Good. The highest power of x is 3, so the degree of the expression is 3.
Your cards say 3x, −5y, 7x, 2xy, −x, 4y, 6xy and 9. Put like terms together.
The x-terms are 3x, 7x and −x. Together they make 9x.
The y-terms, −5y and 4y, make −y, and 2xy and 6xy make 8xy.
So the whole set simplifies to what?
9x − y + 8xy + 9.
Can we combine 9x and 8xy?
No. They have different variable parts, so they are unlike terms.
One square takes 4 matchsticks, two squares in a row take 7 and three take 10. What do you notice?
Each new square adds 3 sticks, because it shares one side with the square before.
So how many sticks for n squares?
3n + 1. The 1 is the first side, and each square adds 3 more.
Use it for 10 squares.
3 times 10 plus 1, which is 31 sticks. Much faster than building them all!
an expression splits into terms at plus and minus signs, and each sign belongs to the term after it.
the coefficient multiplies the variable part, and the constant term has no variable.
only like terms can be combined, by adding or subtracting their coefficients.
a growing pattern, such as squares made of matchsticks, can be described by an expression like 3n + 1.
replacing a variable by a number and simplifying gives the value of an expression.
the highest power is the degree, and one, two and three terms make a monomial, binomial and trinomial.
5x³ − 2x² + 7x − 4 has four terms, coefficients 5, −2 and 7, the constant term −4 and degree 3.
3x + 7x − x − 5y + 4y simplifies to 9x − y, because only like terms are combined.
A row of n matchstick squares needs 3n + 1 sticks, so 10 squares need 3 × 10 + 1 = 31 sticks.
The value of 2x² − 3x + 5 when x = −1 is 2(1) + 3 + 5 = 10.
The sign in front goes with the term, to find a coefficient, that's what you learn.
In Algebra Town, the x-family, the y-family and the xy-family each lived on their own street. At census time, the officer counted each street separately, because you cannot add an x to a y, just as you cannot add apples to bananas.
"Same letters, same powers, same family": only like terms can be added together.
T.C.C.D. - Terms, Coefficients, Constant, Degree: the four things to find in any expression.
Term
How many terms are there in 5x³ − 2x² + 7x − 4?
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Term
What is the coefficient of x² in 5x³ − 2x² + 7x − 4?
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Term
Are xy and yx like terms?
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Term
How many matchsticks are needed for n squares in a row?
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Term
What is the degree of 5x³ − 2x² + 7x − 4?
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A part of an expression separated from other parts by a plus or minus sign, such as −2x².
The number multiplying the variable part of a term, including its sign; in −2x², it is −2.
A term with no variable, such as −4 in 5x³ − 2x² + 7x − 4.
Terms with exactly the same variables raised to the same powers, such as 3x and −x.
Terms whose variable parts differ, such as 9x and 8xy, which cannot be combined.
The highest power of the variable in an expression; 5x³ − 2x² + 7x − 4 has degree 3. For a term with more than one variable, add the powers of its variables: 7x²y has degree 2 + 1 = 3.
An expression with one term, such as 7x²y.
An expression with two terms, such as 4m − 9.
Hands-on activities that build a working understanding of algebraic expressions: breaking an expression into terms, sorting like terms, turning patterns into expressions, and finding the value of an expression.
This lesson is built around five short activities. You hunt for the terms, coefficients and constant in 5x³ − 2x² + 7x − 4; sort a set of term cards into like terms and simplify them; discover the expression behind a matchstick pattern; substitute numbers into an expression to find its value; and write expressions for the perimeter and area of a rectangle whose sides are given in algebra. Along the way you meet the degree of an expression and the names monomial, binomial and trinomial.
Break 5x³ − 2x² + 7x − 4 into its terms. The sign in front of each term belongs to that term.
So the expression has four terms. The coefficients are 5, −2 and 7, and the constant term is −4, which has no variable. The highest power of x is 3, so the degree of the expression is 3.
Write these terms on cards: 3x, −5y, 7x, 2xy, −x, 4y, 6xy, 9. Sort them into groups of like terms, which have exactly the same variables raised to the same powers.
Together they simplify to 9x − y + 8xy + 9. Unlike terms, such as 9x and 8xy, cannot be combined. Note that x and x² are unlike, but xy and yx are like terms, because xy = yx.
Make squares in a row with matchsticks, so that neighbouring squares share a side.
A row of triangles works the same way: 1 triangle needs 3 sticks and each new one adds 2, so n triangles need 2n + 1 sticks.
To evaluate an expression, replace the variable by the number and simplify, doing powers first, then multiplication, then addition and subtraction. For 2x² − 3x + 5:
A rectangle has length (2a + 3) cm and breadth a cm.
An expression with one term is a monomial (such as 7x²y), with two terms a binomial (such as 4m − 9) and with three terms a trinomial (such as a³ − 2a + 6). An expression like 5x³ − 2x² + 7x − 4, with four terms, is simply called a polynomial.