NCTB Class 7 Math Chapter Five Exercise 5.1 Solution

NCTB Class 7 Math Chapter Five Exercise 5.1 Solution by Math Expert. Bangladesh Board Class 7 Math Solution Chapter 5.1 “Algebraic Formulaic and Applications” Exercise 5.1 Solution.

Board

NCTB
Class

7

Subject

Math
Chapter

5

Chapter Name

“Algebraic Formulaic and Applications”
Exercise

5.1 Solution

Exercise:- 5.1

(1) Solution:- (a+5)2

= a2+2x z x 5+52

= a2+10a+25

(2) Solution:- (5x-7)2

= (5x)2 – 2x5xX7+ (7)2

= 25x2-70x+49

(3) Solution:- (3a-11xy)2

= (3a)2 – 2x3ax11xy+ (11xy)2

= 9a2– 66axy+ 121x2 y2

(4) Solution:- (5a2+9m2)2

= (5a2)2+2x5a2.9m2+ (9m2)2

= 25a4+ 90a2 m2+ 81 m4

(5) Solution:-  (55)2

= (50+5)2

= (50)2+ 2x50x5 +52

= 2500+500+25

= 3025

(6) Solution:-  (990)2

= (1000-10)2

= (1000)2 – 2x1000x10+(10)2

= 1000000-20000+100

= 980100

(7) Solution:- (xy-6y)2

= (x y)2– 2.xy.6y+ (6y)2

= x2 y2– 12xy2 +30y2

(8) Solution:- (a x-by)2

= (a x)2– 2.ax.by + (by)2

= a2 x2– 2axby + b2 y2

(9) Solution:- (97)2

= (100-3)2

=  (100)2– 2.100.3+ 32

= 10000- 600+9

= 9409

(10) Solution:- (2x+y-z)2

= {(2x+y)-z}2

= (2x+y)2 – 2. (2x+y).z+ z2

= (2x)2 +  2X2xXy+y2– 4zx-2yz+z2

= 4x2+4xy+y2-4zx-2yz+x2

(11) Solution:- (2a-b+3c)2

= {(2a-b)+ 3c}2

= (2a-b)2+2. (2a-b).3c+(3c)2

= (2a)2– 2.2a.b.+b2+12ac-6bc+9c2

= 4a2-4ab+b2+12ac-6bc+9c2

= 4a2+b2+9c2-4ab+12ac-6bc

(13) Solution:- (x2+y2-z2)2

= {(x2+y2)2 – (z2)2}

= (x2+y2)2– 2. (x2+y2). Z2 + (z2)2

= (x2)2+ 2x2y2+ (y2)2– 2x2 z2 – 2y2 z2+ z4

= x4+y4+z4+2x2 y2+ 2y2 z2– 2z2 x2

(14) Solution:- (3x-2y+z)2

= {(3x-2y) + z}2

= (3x-2y)2+ 2. (3x-2y) . z +z2}

= 9x2-12xy+4y2+6xz-4yz+z2

= 9x2+4y2+z2+12xy+6xz-4yz

(15) Solution:- (b c +ca +a b)2

= {(b c +c a) + a b}2

= (b c+ c a)2 + 2. (b c +c a). a b+ (a b)2}

= (b c)2+2.bc.ca+ (ca)2 + 2ab2c +2a2bc+ a2 b2

=b2c2+ c2a2+a2b2+ 2ac2+2ab2c+2a2bc

(17) Solution:- (2a+1)2 – 4a(2a+1)+ 4a2

= (2a1)2– 2. (2a+1). 2a + (2a)2

= {(2a+1) – 2a}2

= (2a+1-2a)2

= (1)2 = 1

(18) Solution:-  Let, 5a+3b= x ; 4a-3b= y

Given, x2+2xy+y2

= (x +y)2

= (5a+3b+4a-3b)2

= (9a)2

= 81a2

(19) Solution:- Let, 7a+b= x ; 7a-b= y

Therefore, given, x2-2xy+y2

= (x-y)2

= (7a+b-7a+b)2

= (2b)2

= 4b2

(20) Solution:- Let, (2x+3y)= a ; 2x-3y= b

Given, a2+ 2ab+b2

= (a +b)2

= (2x+3y+2x-3y)2

= (4x)2

= 16x2

(21) Solution:- (5x-2) = a ; 5x+7= b

Given, a2+b2- 2ab

= (a-b)2

= (5x-2-5x-7)2

= (-9)2

= 81

(22) Solution:- (3ab-cd)2 + 9 (c d-a b) + 6 (3ab-cd) (c d-a b)

= (3ab-cd)2 + 2. (3ab-cd) x 3 (c d-a b) + [3 (c d- a b)]2

Let, 3ab-cd= x ; 3 (c d-a b) = y

Therefore, x2+ 2xy +y2

= (x +y)2

= {(3ab-cd) +3 (c d-a b)}2

= (3ab-cd+3cd-3ab)2

= (2cd)2

= 4c2d2

(23) Solution:- (2x+5y+3z)2 + (5y+3z-x)2- 2 (5y+3z-x) (2x+5y+3z)

Let, (2x+5y+3z) = a ; 5y+3z-x = b

Therefore, a2+b2-2a b

= (a-b)2

= {2x+5y+3z-5y-3z+x}2

= (3x)2

= 9x2

(24) Solution:- (2a-3b+4c)2 + (2a+3b-4c)2 + 2 (2a-3b+4c) (2a+3b-4c)

Therefore, Let, 2a-3b+4c= x and, (2a+3b-4c) = y

Therefore, x2+ y2+2xy

= (x +y)2

= (2a-3b+4c+2a+3b-4c)2

= (4a)2

= 16a2

(25) Solution:- 25x2+36y2– 60xy ; when x= -4, y= -5

Therefore, 25x2 + 36y2– 60xy

= (5x)2 + 2.5x.6y+ (6y)2

= (5x-6y)2

= {5(-4) -6 (-5)}2

= (-20+30)2

= (10)2 = 100

(26) Solution:- 16a2– 24ab- 9b2

= (4a)2 – 2.4a.3b+ (3b)2

= (4a-3b)2

= (4×7-3×6)2

= (28-18)2

= (10)2

= 100

(27) Solution:- (9x2+30x+25)

= (3x)2+2.3x.5+52

= (3x+5)2

= {3x (-2) + 5}2

= (-6+5)2

= (-1)2

=1

(28) Solution:- 81a3+18ac+c2

= (9a)2+ 2.9a.1 +c2

= (9a+c)2

= ({9×7-67}2

= (63-67)2

= (-4)2

= 16

(29) Solution:- a2+ b2= (a +b)2– 2ab

= (5)2– 2x 12

= 25-24

= 1

(31) Solution:- x+ 1/x = 5 (given)

=> (x+1/x)2= (5)2

=> x2+ 1/x2 = 25-2

= x2+ 1/x2 = 23

Both side square,

(x2+1/x2)2 = (23)2

=> (x2-1/x2)2 + 4.x2. 1/x2= 529

=> (x2– 1/x2)

= 529-4

= 525

(32) Solution:- a +b= 8: a-b- 4

We know that,

4ab= (a +b)2 – (a -b)2

= 82– 42

= 64-16

= 48

Therefore, a b= 12

Updated: December 16, 2020 — 8:47 am

13 Comments

Add a Comment
  1. Where is 33 and 34 ??

    1. Wait available soon

  2. Sir 22 Number is it correct? Because,, I’m little bit confused.
    Reason is,, In Text book the question is different. Kindly reply me.In this pandemic situation our only trust and options is Online.And when I solve this question.I face problem just only this question.In the Text book The question like this,,,
    (3ab-cd)^2 + 9(cd-ab)^2+6(3ab-cd)(cb-ab)❓❓
    ⭕️⭕️ ^2 It means (Hole Square)
    Please reply as soon as possible.
    Thank you ????

    1. Joty please tell Question number. We will solve your doubt

      1. 5.1 Question no.(22)

  3. Pls send 33 and 34 fast.

  4. JANNATUL SABRINA CHAWDURY J

    There is no solution of 33 and 34.

    1. Where is namber33.34????

  5. 5.1 Question no.(22)

  6. Tahmid Hasan Tasfi

    Where r the solutions of 33 & 34

    1. Tahmid will available soon

  7. Yousof arafat abir

    Where is 30 no solution sir

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