How to represent geometrically quadratic expression x² + 5x + 6
Channel: Mathematics Learning
Date: 2020-07-24

#Algebraicexpressions #Class8Mathematics #Mathematicslearning 
Geometrical representation of quadratic expression x² + bx + c

Example x² + 5x + 6


Class 8 Mathematics Ch 7 Algebraic Identities

Algebraic Expressions|Variable|Constant|Operations|Terms|Coefficient|Monomial|Binomial|Trinomial|Identity|Algebraic identity (a+b)2 https://youtu.be/YDbzJYOPawo
Algebraic Identities https://youtu.be/rL3YQ9KYH6k

Identity 1: (a+b)2  WS1 Q1 https://youtu.be/EYsEUbTSSNA
Identity 1: (a+b)2  WS1 Q2 https://youtu.be/o_DUshFTN0Y
Identity 2: (a-b)2WS2 Q1 Find the following (i) (x-7)²(ii) (5a-4b)²(iii) ((7x/4)-(2y/3))²  https://youtu.be/1lw5jx4eFnY 
Identity 2: (a-b)2 WS2 Q2 Evaluate the following using identity (i) (48)²(ii) (9.9)²(iii) (299)²
https://youtu.be/wzLomO-GTUg
WS3 Discussion of all problems based on identity 3: a² -b²  = (a-b)(a+b)   https://youtu.be/DP7J2LGBTqk 
Type 1 - Find the product
(i) (2x+7y)(2x-7y) (ii)(5ab-8c)(5ab+8ac) 
(iii) (4p² + q²)(4p² - q²) (iv) (x/3 -y/2)(x/3+y/2)
Type 2- Evaluate (i)(81² - 19²) (ii)(290² - 210²) 
(iii) (58² - 12²) (iv)(176² - 24²) (v) (367² - 33²) (vi)(545² - 445²)
Type 3- Simplify (i) 107 x 93 (ii) 211 x 189 (iii) 195x205
(iv) 308x292 (v) 12.4x11.6 (vi) 30.9x29.1
WS3 Q1 Find the product
(i) (2x+7y)(2x-7y) (ii)(5ab-8c)(5ab+8ac) 
(iii) (4p² + q²)(4p² - q²) (iv) (x/3 -y/2)(x/3+y/2)
https://youtu.be/oyPObsO9f0g
WS3 Q2 Evaluate (i) (81)²-(19)² (ii) (290)²-(210)² (iii) (58)²-(12)²
 https://youtu.be/qQsSsTWQY9o
WS4 Expand the following  https://youtu.be/KcBrHDx-378
 (i) (x-2y+3z)²
(ii) (-5x+2y+z)²
(iii) (4x+y-3z)²
(iv) (3a-5b-7c)²
(v) (-2a-b+3c)²   
WS4 Q1  (i) (x-2y+3z)²    https://youtu.be/ghJ0zpINnls
WS4 Q2 (ii) (-5x+2y+z)² https://youtu.be/mLTtPN8CWCY
WS5 Find the product by using suitable identity https://youtu.be/MC6mmK22Vrs 
(i) (x+5)(x+4)
(ii) (a+3)(a+6)
(iii) (x-9)(x+7) 

Geometrical representation of algebraic identity (a+b)² = (a² + 2ab + b²)https://youtu.be/MR8muglizrc 

 
Geometrical representation and verification of algebraic identity (a-b)² = (a² - 2ab + b²)https://youtu.be/jwV9YbasR6g 

Geometrical representation and verification of algebraic identity a² -b² = (a+b)(a-b)  https://youtu.be/Xv3mbMCTC4c 
Geometrical representation of algebraic identity (a+b+c)² https://youtu.be/bmFvxThC6RU 
How to factorise algebraic expression of type x² + bx + c using Splitting the middle term  https://youtu.be/AXREjUHty9Y 
 



Brain Teasers
Q1 B (a) Find the product using suitable identity.(a+3) (a-3)(a² +9) https://youtu.be/x8lzbHA9BMA 
Q1 B (b) If  x^2 + 1/x^2  = 6 , find x^4 + 1/x^4  https://youtu.be/Tw23nWBPa98 
Q1 B (c) Find the value of k if  xy²k = 4(4x+3y)²-(4x-3y)²   https://youtu.be/ki34r82aarM 
Q2 (vi) Find the product using suitable identity  [x+1/x][x-1/x][x²+1/x²][x⁴+1/x⁴]  https://youtu.be/4DqYaRWIM8w 
Q6 Evaluate x
(i)if 36x =78²-42²
(ii)6.2x =8.1x8.1-1.9x1.9
 https://youtu.be/BKtlA-vNePc 
Q8 if x+1/x = 8 then find x²+1/x²   https://youtu.be/sZJf_Cy0ULY 
Q13 if 3x - 4y = 10 and xy = -1 then find the value of 9x²+16y²  https://youtu.be/58UdnT7Ywzw 
Q14  If 5x-2y= 7 and xy=2 , find the value of (5x+2y)²    https://youtu.be/5W91sZTLRIE 
Q15 https://youtu.be/IFJeum1NAsM 

Practice Questions

if x+1/x = 5 then find x²+1/x²   https://youtu.be/xAy7xXtGdGM 
Factorise (4a)² -(b-c)²   https://youtu.be/s-o2DQLYy9k 
Show that.
 (i) (3x + 7)² – 84x = (3x – 7)²
 (ii) (9p – 5q)²+ 180pq = (9p + 5q)²
 (iii) (4pq + 3q)²– (4pq – 3q)² = 48pq²
 (iv) (a – b) (a + b) + (b – c) (b + c)+ (c – a) (c + a) = 0 
https://youtu.be/eE2SuMTQP9M 



Hands on activities
Verification of (a+b+c)^2 https://youtu.be/REzurdsaJZU 
Verification of (a^2 - b^2) https://youtu.be/rTkI2kvhQHI 
Visualisation of x^2+5x+6  https://youtu.be/DzLxUiCT0vc 

Maths Quiz https://youtu.be/wOg_kXJOysc