Which of the following is an expression?
An algebraic expression include constants, variables and coefficients, so answer is 4x+7
Which of the following is a binomial?
A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial. Binomials are used in algebra.
For option a) there are three terms in the expression i.e. 7, 3x and 4
For option c) there are three terms as well i.e. 4x, y and 2.
For option d) there is only one term i.e. 3x
For option b) there are two terms i.e 2x and 7. Therefore it is a binomial.
Notice Bi means 2 so a binomial has 2 terms.
Add: 7xy + 5yz – 3zx, 4yz + 9zx – 4y, –3xz + 5x – 2xy.
Writing the three expressions in separate rows, with like terms one below the other, we have
7xy + 5yz – 3zx
+ 4yz + 9zx – 4y
+ –2xy – 3zx + 5x

= 5xy + 9yz + 3zx + 5x – 4y
Thus, the sum of the expressions is 5xy + 9yz + 3zx + 5x – 4y. Note how the terms, – 4y
in the second expression and 5x in the third expression, are carried over as they are, since
they have no like terms in the other expressions.
Expression that contains only one term is called a __________.
Simplify: (xy + yz)^{2}− (xy − yz)^{2}
(xy+yz)²(xyyz)²
xy² +yz² +2.xy.yz (xy²+yz²2xy.yz)
(xy)² +(yz)² +2xy²z [(xy)² +(yz)² 2xy²z
(xy)² +(yz)² +2xy²z (xy²)(yz)² + 2xy²z
Cancelled (xy)² +(yz)² and (xy²)(yz)².
2xy²z+ 2xy²z
=> 4xy²z
Hence, Value of (xy + yz)² – (xy – yz)² => 4xy²z
Note;
(a+b)²(ab)² = 4ab
Simplify(xy + yz)^{2}− 2x^{2}y^{2}z. Find the value when x = 1, y = 1 and z = 2.
Using identity (x  a) (x + a) = x^{2}  a^{2} find 5^{2 }− 4^{2}.
x^{2}  a^{2} = ( x + a) (x  a) using this equation.
5^{2}  4^{2} = ( 5 + 4) ( 5  4 )= ( 9 ) (1 )= 9
Using identity (x − a) (x + a) = x^{2 }− a^{2} find 6^{2 }− 5^{2}.
To find: 6^{2}  5^{2}:
Putting x = 6 and a = 5 in identity x^{2}  a^{2 }= (x  a)(x+a);
⇒ 6^{2} 5^{2} = (6  5)(6 + 5) = 11.
Terms are added to form ___________.
Terms include variables,constants and coefficients which when added forms an expression.
Which of the following is like term as 7xy?
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