Algebriac Expression

8/13/2019 Algebriac Expression

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1Class-7th


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S.No. Term NumeralCoefficient

Literal

Coefficient1 4x 4 x2 -7xy -7 xy

Algebraic Expressions%&Monomial 6ab

Binomial 3x + 7

Trinomial x2y3+ z3

Previous Knowledge


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When we combine numbers and literal

numbers by means of Arithmetic operations

we get Algebraic expressions .

For example,

Number = 2

Literal Number = x

Hence 2x is a Algebraic expressions

Algebraic Expressions


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Multiplication of Monomials

Multiplication of a Monomial and Binomial

Multiplication of Binomials

Multiplication of a Binomial and a Trinomial

Standard Identities

Quiz and Question -Answer

Things to Remember

To teach manipulation of algebraic expressions to studentsthrough the use of geometrical representations:

Objectives


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A B

CD

12x2

4x

3x

Product of monomials are represented by area of a rectangle

ABCD

Multiplication of Monomials


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Binomial:-

Every binomial is a sum or difference

of two monomials.

If we take a monomial ( k ) and a Binomial

(x+y). Let us draw a rectangle ABCD whose length

and breadth are (x+y), k respectively.Take a point P on line AB such that AP= x

and PB = y. From P , draw a line PQAD meetingDC in Q.

Multiplication of Monomialby Binomial


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Area of APQD

k(x+y)

Hence k(x+y) is represented by area of rectangle ABCD.

Area of PBCQ

A B

CD Q

Multiplication of Monomialby Binomial

+

= kx + ky

SinceArea of rectangle ABCD =Area of APQD Area of PBCQ

x y

k

P

k(x+y) kx kyArea of rectangle ABCD


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If P,Q,R, S are monomials and (P+Q),(R+S)

are binomials. Draw a rectangle ABCD whose sides

are (P+Q) and (R+S). Then the product of binomial(P+Q) and (R+S) are represented by area of rectangle

ABCD.

Area of ABCD =

=Area of AGIF +Area of GIED+Area of FBHI +Area

of HCEI

Multiplication of Binomialby Binomial


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=Q

PRPS

QRQS

R

P+Q

S

P

(P+Q)(R+S) PR QSQRPS= $ $$

(P+Q)(R+S)

A B

CD E

FA B

CD

G I

Multiplication of Binomial

by Binomial

R+S H

P

HenceMultiplication of Binomial (P+Q)(R+S) is represented by Area of

{ AGIF + GIED + FBHI + HCEI }


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ay az bx by bz

=x+y+zA B

CD

A B

CD

EF

x z

a

y

G

H

I

J

K L

b

(a+b)(x+y+z) = ax+ + + + +

Multiplication of Binomial

by Trinomial

a+b

HenceMultiplication binomial (a + b) and Trinomial (x +y +z) is equal to

Area of rectangles {AHKE +HJLK +JBFL +GKED +ILKG +CFLI }


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(a+b)(a+b) or (a+b)2

(a-b)(a-b) or (a-b)2

(a+b)(a-b) or (a2

-b2

)

(a+b) and (a-b) are two simple binomials. Ifwe multiply each of them with itself andwith other, we get :

Standard Identity


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a+b

a+b

a

b

b

b

a

(a+b)2= a2+ 2ab + b2

b

Cut a squareof side a

Cut a square of side b

Cut a rectangle of lengtha and breadth b

Draw a square of side (a+b)


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(a+b)2= a2+ 2ab + b2

a AArea of Square A is a2

Area of rectangle C is ab

Area of square B is b2

Area of rectangle D is ba

b Cb

Bb

Dab

Know the area of Figure A,B,C,D


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a2+ 2ab + b2= (a+b)2b

a

ab

aa

bb

A B

C D

Joint the Figure A,B,C,D


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a2+ 2ab + b2= (a+b)2a

a

ba

bba

b

A B

C D


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a2+ 2ab + b2= (a+b)2a

a

ba

b

bab

B

C D

A


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a2+ 2ab + b2= (a+b)2a

a

ba

bb

ab

A

D

B

C


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a2+ 2ab + b2= (a+b)2a

a

ba

bb

ab

A B

CD


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a2+ 2ab + b2= (a+b)2a

a

ba

b

b

ab

DA

C

B


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a2+ 2ab + b2= (a+b)2a

a

ba

bba

b C DA B


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a2+ 2ab + b2= (a+b)2

a+b

a+b


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(a+b)2= a2+ 2ab + b2

a+b

a+b

a+b

a+b=

Hence Identity ( a+b)2 = a2 + 2ab + b2

A B C D

A BC D


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a

a

a-b

a-b

(a-b)2=a22ab +b2

a-b

b

b

b

b

b

a-b

b

A B

CD Area of square ABCD isa2Area of this square is

(a-b)(a-b)=(a-b)2Area of this rectangle is

b(a-b) Area of this rectangle is(a-b)b

Area of this square isb

2

Draw a Square of side a


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(a-b)2=a22ab +b2

A

B C

Joint figure A,B,C


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(a-b)2=a22ab +b2

A

BC


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(a-b)2=a22ab +b2

A

BC


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(a2-b2) =(a+b)(a-b)

a

a

b

a-b

a-b

Area of Square ABCD is"a2Area of figure AGFECDis (a2-b2)

A B

CDCut a square EFGB ,of side

b, area of square is b2

EF

Ga-b

H

Cut a rectangle FECH and paste it on

top breath of the rectangle AGHD withheight (a-b) of rectangle FECHI J

a+b

Here a and b are two monomials.


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(a2-b2) =(a+b)(a-b)Area of this figure is(a2-b2)

=

a-b

a+b

Hence

(a2

-b2

) =(a+b)(a-b)

ab

a Area of this rectangle is(a+b)(a-b)


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Quiz About

Algebraic Expressions

{Click on the right answer andcheck your understanding}


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Question 1Multiply 6ab and -7bc:

A. [- 42abc]

C. [42ab2c]

B. [13ab2c]

D.[-42ab2c]


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Question 2Find the product (5xy)(x3y2)(6):

A. [11x4y3]

C. [30x3y4]

B. [11x3y4]

D. [30x4y3]

Q ti 3


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A. [2x2-x-3]

C. [2x2+x+3]

B. [2x2+x-3]

Question 3Multiply (x-1) and(2x+3):

D. [2x2-5x+3]


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Question 4Which of the following is a suitable

Identity to multiply (3x-4y) and (3x-4y):

A. (a-b)2=a2+b2 -2ab B. (a-b)(a+b)=a2- b2

D. None of the aboveC. (a+b)2=a2+b2+2ab

and the correct answer of the multiplication is:

A. 9x2+16y2-24xy B. 3x2-12xy+4y2

D. None of the aboveC. 9x2+24xy+16y2

Q 5 Whi h f th f ll i i


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Question 5 Which of the following is asuitable Identity to multiply (2p+5q)

and (2p+5q):

A. (a-b)2=a2-2ab+b2

C. a2-b2=(a+b)(a-b)

B. (a+b)2=a2+2ab+b2

None of the above

and the correct answer of the multiplication is:

A. 4p2+20pq+25q2 B. 2p2+10pq+q2

D. None of the aboveC. 4p2-20pq-25q2


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Questions and AnswersFind the product of following :

Solutions

6. (5a2b)(3b2c)(4ac2)

7. (x+y)(7x-y), x = 1,y = 0 multiply

and verify the result for given

values:

8. (x+2y)(2x-9y+7)

9. 992,using the suitable identity:

10.(512 - 492) Evaluate without

calculating the square of any

number:


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Solutions6. (5a2b)(3b2c)(4ac2)

7. (x+y)(7x-y), x = 1,y = 0 multiply

and verify the result for given

values:

8. (x+2y)(2x-9y+7)

9. 992,using the suitable Identity:

10.(512 - 492) Evaluate without

calculating the square of any

number:

Ans.6.={534}{a2+1b1+2c1+2}

= 60a3b3c3= 60a3b3c3

Ans.7.= x(7x-y) + y(7x-y)

=7x2xy+7xyy2 = 7x2+6xy-y2

Put x = 1 and y = 0, = 7(1)2- 10 + 710 - (0)2

= 710 + 0 -0 = 7

Ans.8.= x(2x-9y+7) + 2y(2x-9y+7)

= 2x2 - 9xy + 7x + 4xy - 18y2+ 4y

= 2x25xy + 7x + 4y - 18y2

Ans.9. = 992

Use Identity (a-b)2= a2 -2ab +b2

= (100 -1)2 = (100)2- 21001 + (1)2

=10000 - 200 +1 = 9801

Ans.10. = 512492

Use Identity a2b2= (a+b)(a-b)

=512 492 = (51+49)(51-49)

= 1002 = 200


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Things To RememberThe Product of two monomials is the product of their coefficients and the

literals in the two monomials, the exponent of each literal being the sum of the

exponents in the given monomials.

To multiply a monomial by a binomial ,we multiply the monomial with each

term of the binomial and add the product.

To multiply two binomials, we multiply each term of one binomial with each

of the other and add the products.

To multiply a binomial and a trinomial, we multiply each term of the

binomial with each term of the trinomial and add the products.

Useful Identities:For all values of a and b.

(a+b)2 = a2 + 2ab + b2

(a-b)2 = a2- 2ab + b2

2 b2 ( +b)( b)

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Algebriac Expression