Summary on the last page
ANSWER KEY - ALGEBRA
I. Write algebraic expressions for the following
a. 3x subtracted from 89 = 89 – 3x(since it is from 89)
b. 5x decreased by 7 = 5x-7
c. 9x added to 6y = 9x + 6y
d. Three fourth of l = 3/4 l
e. 5 times m divided by 3 times n = 5m/3n
II.
Separate the constants and variables in the following terms
a. 256x2z - Constant – 256; Variable - x2z
b. 56 - Constant – 56 ; No Variable
c. 73y2 - Constant – 73; Variable - y2
d. z2 - Constant – 1 ; Variable - z2
e. 2x2 - Constant -2 ; Variable - x2
III.
Write the terms in each of the following expressions
a. -8x3y + 2xyz- 4x2 - Terms are 8x3y, 2xyz, - 4x2
b. lmn + 3l2m2 - 5m2n2 - Terms are lmn, 3l2m2, - 5m2n2
c. 5a2b – 15abc +3ab2c - Terms are 5a2b, – 15abc, 3ab2c
d. -25p2 – 6q2+pqn - Terms are -25p2, – 6q2, pqn
e. 15de – def +2d2c – Terms are 15de , -def, 2 d2c
IV.
Write algebraic expressions using the following terms
a. –x2y , 3xy, xyz - Expression -
–x2y +3xy+ xyz
b. 2 m2n , -2mn, - 5 mnk - Expression - 2/3m2n – 2mn – 5mnk
3
c. -12a2b , +5abc , -4a2c2 - Expression - 5abc -4a2c2 -12a2b
Note - Terms can be arranged in any order but the sign must be carried along with the
term
Summary on the last page
V.
Write true or false and correct the false sentences
a. The coefficient of x in 13xy2z is 13 - False
Correct statement – The coefficient of x in 13xy2z is 13y2z
b. a4z2 = 4*a*z*z - False
Correct Statement – a*a*a*a*z*z
c. 4x2y + 5d ÷3e is a trinomial - False
Correct Statement - 4x2y + 5d ÷3e is a binomial since 5d/3e is one term
d. In – 9z2y ; -9 is the constant – True
VI. Identify the type of algebraic expression
a. 2a+n – 8 ÷ y - Trinomial – Three terms (8/y is one term)
b. 23a ÷ 9 -
Monomial – One term
c. x + y ÷ a -
Binomial – Two terms ( y/a is one term)
d. ax2 – x +5 -
Trinomial – Three terms
e. x + xy – y2 -
Trinomial – Three terms
VII.
Write the coefficient of
a. x2 in -3x2y - Coefficient is -3y
b. d2e2 in – 32d2e2f - Coefficient is -32f
c. m2 in – 15m2n - Coefficient is -15n
VIII.
Write the numeral coefficient in the following terms
a. -36x2y Literal coefficient – x2y
Numeral coefficient - -36
b. 200a2bc -
Summary on the last page
Literal coefficient – a2bc
Numeral coefficient - 200
c. -2p2q2y
Literal coefficient - p2q2y
Numeral coefficient - -2
IX. Write the factors of
a. 56x2yz -
56, x, x, y, z
b. -2p2q2r -
-2, p, p, q, q, r
c. -25lmn2 -
-25, l, m, n, n
X. Write in order by arranging numeral factors and literal factors in alphabetical
order.
a. 3vd6m – 18dvm
b. lex34 – 12elx
c. 2pmn6 – 12mnp
XI. Identify like and unlike terms in the following
a. 4x, -3y2, -x, 2x, 4y, y3
3 5
Like terms – 4x, -x, 2/3x
Unlike terms - -3y2, 4y/5, y3
b. 2xy, -4yx, 2y2z, -2yz2, yx
3
3
Like terms – 2xy/3, -4yx, yx
Unlike terms – 2y2z, -2/3yz2
c. –ab2, b2a2, 7b2a, -3ab2, 2ab3
Like terms - -ab2 , -3ab2, 7b2a
Summary on the last page
Unlike terms - b2a2, 2ab3
XII.
Substitute and find the value of the following algebraic expressions
a. n – 2m +l where n= 16; m =4 and l = 6
= 16 – 2*4 + 6
= 16 – 8+6
=16 – 2
=14
Answer = 14
b. 5x – 3z where x = 9 and z = 5
=5*9 – 3*5
= 45 – 15
= 30
Answer = 30
c. 6m +9n-3k where m = 2, n =1 , k = 6
=6*2 +9*1 – 3*6
= 12+9 – 18
=21 -18
=3
Answer = 3
XIII.
Expand the following
a. a3m2n = a*a*a*m*m*n
b. x4yz2 = x*x*x*x*y*z*z
c. p2qrs3 = p*p*q*r*s*s*s
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Summary on the last page
SUMMARY – ALGEBRA
Constants – Numbers in an algebraic term
Example - 2, 9, 5, 6 ………..
7
Variables – Alphabets in an algebraic term
Example - x, y, I, j …………
Expression – Combination of Numbers and variables
Example - 3x, 4+z, 2-z
Terms – many terms together form expression
Example - 2x – 3y +4z ; here 2x, -3y, +4z are terms
Writing expression from statements
Example :
3 decreased by a = 3-a
3 decreased from a = a- 3
3 multiplied by u = 13*u = 13u
15 divided by z = 15
Z
Types of algebraic expression
Monomial – Algebraic expression has one term
Examples :
2x2
5÷ 2a
Binomial – Algebraic expression has two terms
Example :
3x +2y
Trinomial – Algebraic expression has three terms
Example :
3a2+5b – 2c
Quadrinomial – Algebraic expression has four or more terms
Example :
4a – 6d +5m2 -3
Summary on the last page
Coefficients
Example :
Coefficient of x2 in 3x2yz = 3yz
Coefficient of y in 3x2yz = 3x2z
Coefficient of 3 in 3x2yz = x2yz
Coefficient of z in 3x2yz = 3x2y
Type of Coefficients
Numeral coefficient – number
Literal coefficient – alphabet
Example :
Numeral coefficient of – xyz = -1
Literal coefficient of –xyz = xyz
Numeral coefficient of -9x3yz = -9
Literal coefficient of -9x3yz = x3yz
Writing expressions with the given terms
Example:
Terms are -9x, -8ab, xy, 5z
Expression is -9x-8ab+xy+5z
Write the factors of
Example :
12a2b
4xy
mnu
2p2q2z2
=
=
=
=
12, a2 , b
4, x, y
m, n, u
2, p2, q2, z2
Rearrange numeral and alphabetic factors
3xa2y = 6axy (i.e. 3*2 =6 and then literal factors arranged in alphabetical
order)
5uvn4 = 20nuv
4lnu3d = 12dlnu
Like terms – Must have same literal factors
Numerical factors need not be the same
Example - 4x2y, 3x2y , 2x2y (x2y is common in every term)
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Unlike terms – Must have different literal factors
Numeral factors could be the same or different
Example – 4xyz, 4x2y, 4yza (literal factors are different in every term – xyz,x2y,yza)
Substitution – substitute with the given value
Example
5x – 2a +6q where x = 2, a=3, q=4
= 5*2 – 2*3 +6*4
= 10 -6 +24
= 28
Expansion
Since it is a to the power of 3; so a multiplied 3 times
Example
Since it is c to the power of 1 ; so c multiplied one time
m4a3d2c = m*m*m*m*a*a*a*d*d*c
Since it is d to the power of 2 ; so d multiplied 2 times
Since it is m to the power of 4; so m multiplied 4 times
Important Note: m4 does not mean 4 * m it is m*m*m*m
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