Various types of algebraic expressions are as follows:
Eg. \(4x,\; 3y,\; 6z\), etc.
Eg. \(x^2+4x,\;y+4,\;3x+4\), etc.
Eg. \(x^3+2x+1,\;a^2+b^2+2ab\), etc.
Eg. \(x^2-y^2+6+x,\;x^3+3+6x^2+2x\), etc.
Eg. \(6x^3+x^5+x^4+x^2+x+1\), etc.
\(a+b=b+a\)
2. Commutative Property of Multiplication: On changing the order of numbers, their product does not change. This is known as commutative property of multiplication, i.e.
\(a×b=b×a\)
3. Associative Property of Addition: On changing the grouping of numbers, their sum does not change. This is known as associative property of addition, i.e.
\(a+(b+c)=(a+b)+c\)
4. Associative Property of Multiplication: On changing the grouping of numbers, their product does not change. This is known as associative property of multiplication, i.e.
\(a×(b×c)=(a×b)×c\)
5. Distributive Property of Multiplication over Addition: The distributive property of multiplication over addition states that multiplying a sum by a number gives the same result as multiplying each addend by the number and then adding the product together, i.e.
\(a(b+c)=a×b+a×c\)
6. Distributive Property of Multiplication over Subtraction: The distributive property of multiplication over subtraction is like the distributive property over addition. Either we find out the difference first and then multiply, or we first multiply with each number and then subtract, the result will always be same, i.e.
\(a(b-c)=ab-ac\)
7. Like terms can be added and subtracted.
For example:
Evaluate: \(4s^2\) when \(s=2\)
Here, the variable is \(s\) and its value is given.
Thus, to evaluate, we simply put \(2\) in place of \(s\).
\(4s^2\)
\(=4(2)^2\)
\(=4×4\)
\(=16\)
A \(6x^2+6xy+6x^2y\)
B \(xy+xy+6x\)
C \(6x+6y+6xy\)
D \(x+y+xy\)
For example:
Evaluate: \(a^2b\) for \(a = - 2,\,b=3\)
Here, the variables are \(a\) and \(b\) and their values are given.
Thus to evaluate, we simply put \(-2\) and \(3\) in place of \(a\) and \(b\), respectively.
\(a^2b\)
\(=(-2)^2(3)\)
\(= 4×3\)
\(=12\)
For example:
Evaluate: \(x^2+2xy+y^2\) for \(x=1,\,y=2\)
Here, two variables are used and their values are given.
Thus to evaluate, we simply put the values in place of variables.
\(x^2+2xy+y^2\)
\(=(1)^2+2(1)(2)+(2)^2\)
\(=1+2×2+4\)
\(=1+4+4\)
\(=9\)
For example:
Jillian's father is thrice as old as Jillian. Two times the sum of their ages is the age of Jillian's grandfather. Write the expression for the grandfather's age.
Here, we first assume that Jillian's age is \(x\) years. Then, her father's age will be \(3x\) years.
Two times the sum of their ages \((x+3x)\) is grandfather's age.
Thus, grandfather's age is \(2(x+3x)\).
A \(45a-20-10\)
B \(10a-45-20\)
C \(20a-45-10\)
D \(45a\)
A \(3(b+c)\)
B \(a^2 + 2ab\)
C \(a^2+2ab+3b+3c\)
D \(a^2+2ab+3b\)