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
Where is 33 and 34 ??
Wait available soon
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 ????
Joty please tell Question number. We will solve your doubt
5.1 Question no.(22)
Pls send 33 and 34 fast.
There is no solution of 33 and 34.
Where is namber33.34????
5.1 Question no.(22)
Where r the solutions of 33 & 34
Tahmid will available soon
Where is 30 no solution sir
13Number not correct
can anyone pls solve this problem for me ?
if, a-b=7 & ab=12, now show that, (a+b)²=61