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Unveiling the Magic: Mastering polynomial Factorisation with Algebraic Identities | Grade 9
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Welcome to our captivating YouTube video, where we will embark on an enchanting journey through the realm of factorisation using the mesmerising power of algebraic identities. Get ready to witness the magic unfold as we dive into the world of polynomial factorisation, exploring the incredible techniques that leverage algebraic identities to simplify and unravel complex expressions.
In this video, we will unlock the secrets of various algebraic identities, including the difference of squares, the perfect square trinomial, and the sum and difference of cubes. We will demystify these identities, explaining their origins and showcasing their profound impact on the factorisation process. Through captivating examples and clear explanations, you will gain a deep understanding of how these identities can be harnessed to transform intricate expressions into elegant, factored forms.
With our newfound knowledge of algebraic identities, we will delve into the art of factorising polynomials. You will witness the application of these identities in real-life scenarios as we guide you through step-by-step examples, showcasing how to identify the right identity to use and systematically simplify polynomial expressions. This process will unlock new insights, allowing you to analyse and manipulate polynomials with precision and confidence.
Throughout the video, we will highlight the beauty and elegance of factorisation, demonstrating how algebraic identities offer a powerful toolkit for problem-solving and mathematical exploration. From simplifying polynomial equations to unraveling the structure of complex functions, these factorisation techniques will empower you to tackle challenging mathematical problems with ease.
Our mission is to inspire and empower you with the magic of factorisation using algebraic identities. Whether you are a student seeking to excel in mathematics or a curious mind eager to uncover the secrets of algebraic manipulations, this video will captivate your imagination and ignite your passion for the beauty of mathematics.
Get ready to witness the magic of factorisation as we unveil the power of algebraic identities. Join us on this enchanting journey as we demystify complex expressions, unlock the hidden treasures of polynomials, and master the art of factorisation. Prepare to be spellbound by the elegance and effectiveness of algebraic identities, and let the magic of mathematics unfold before your eyes.
0:00 Intro
1:00 Important algebraic identities which is helpful for doing factorisarion
2:55 find the product(x+7)(x+5)
3:10 find the product(a-3)(a+ 6)
3:50 find the product(pq+5)(pq-5)
4:21 find the product(ab+cd)(ab+cd)
4:55 find the product (-z+3)(-z+a)
6:38 104\times96
6:44 53\times54
7:48 (102)^2
8:00 78\times82
8:40 Factorise using identity 9x^2+6xy+y^2
9:50 Factorise using identity 16y^2- 40ym + 25m^2
10:38 Factorise using identity 9a^2-\\frac{36}{121}b^2
11:30 (a+b+c)^2
11:45 (4a-2b+3c)^2
13:18 factorise 𝟒𝒙^𝟐+𝟗𝒚^𝟐+𝟏𝟔𝒛^𝟐+𝟏𝟐𝒙𝒚−𝟐𝟒𝒚𝒛−𝟏𝟔𝒙𝒛
15:12 Factorise 𝟐𝒙^𝟐+𝒚^𝟐+𝟖𝒛^𝟐−𝟐√𝟐 𝒙𝒚+𝟒√𝟐 𝒚𝒛−𝟖𝒙𝒛
17:11 Cubic Algebraic identities
18:10 Expansion of (𝟑𝒙−𝟒𝒚)^𝟑
19:30 Factorise 𝟖𝒙^𝟑+𝟐𝟕𝒚^𝟑+𝟑𝟔𝒙^𝟐 𝒚+𝟓𝟒𝒙𝒚^𝟐
20:35 a^3+b^3 and a^3-b^3
21:15 factorise 64x^3-125y^3
21:59 factorise 1000m^3-27m^3
22:20 x^3+y^3+z^3-3xyz
25:00 if x+y+z=0 thenx^3+y^3+z^3-=3xyz
25:40 Without actually expanding, find the values of the following (𝟏𝟎)^𝟑+(−𝟕)^𝟑+(−𝟑)^𝟑
26:24 Without actually expanding, find the values of the following (-8)^𝟑+(6)^𝟑+(2)^𝟑
27:05 Which of the following is a monomial having degree 82 ?(a) 𝒚^𝟖𝟐𝟎 (b) 𝟖𝟐𝟎𝒚 (c) 𝒙^𝟖𝟎𝟎 (d) 𝒎^𝟖𝟐
27:54 Find the value of the polynomial 𝟓𝒙−𝟒𝒙^𝟐+𝟑 𝒂𝒕 𝒙=−𝟏
28:42 If xy = 6 and 3x + 2y = 12, compute the value of 𝟗𝒙^𝟐+𝟒𝒚^𝟐
30:27 Zero of the polynomial 𝒑(𝒙)=𝟐𝒙+𝟓 is ________
30:54 If (x – 1) is a factor of 𝟒𝒙^𝟑+𝟑𝒙^𝟐−𝟒𝒙+𝒌, then find the value of k.
32:22 3 + 5 – 8 = 0. Then what is the value of (𝟑)^𝟑+(𝟓)^𝟑+(−𝟖)^𝟑
32:57 \frac{((𝟑𝟔𝟏)^𝟑 + (𝟏𝟑𝟗)^𝟑)}/{((𝟑𝟔𝟏)^𝟐 − 𝟑𝟔𝟏 \times 1𝟑𝟗 +(𝟏𝟑𝟗)^𝟐 )} is
34:40 𝒙+𝒚=𝟑, 𝒙^𝟐+𝒚^𝟐=𝟓. Find the value of xy.
35:44 If 𝐱−𝟏/𝐱=𝟒, evaluate 𝐱^𝟐+𝟏/𝐱^𝟐
36:40 If 𝐱^𝟐+𝟏/𝐱^𝟐 =𝟐𝟕, 𝐟𝐢𝐧𝐝 𝐱+𝟏/𝐱 𝐚𝐧𝐝 𝐱−𝟏/𝐱
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In this video, we will unlock the secrets of various algebraic identities, including the difference of squares, the perfect square trinomial, and the sum and difference of cubes. We will demystify these identities, explaining their origins and showcasing their profound impact on the factorisation process. Through captivating examples and clear explanations, you will gain a deep understanding of how these identities can be harnessed to transform intricate expressions into elegant, factored forms.
With our newfound knowledge of algebraic identities, we will delve into the art of factorising polynomials. You will witness the application of these identities in real-life scenarios as we guide you through step-by-step examples, showcasing how to identify the right identity to use and systematically simplify polynomial expressions. This process will unlock new insights, allowing you to analyse and manipulate polynomials with precision and confidence.
Throughout the video, we will highlight the beauty and elegance of factorisation, demonstrating how algebraic identities offer a powerful toolkit for problem-solving and mathematical exploration. From simplifying polynomial equations to unraveling the structure of complex functions, these factorisation techniques will empower you to tackle challenging mathematical problems with ease.
Our mission is to inspire and empower you with the magic of factorisation using algebraic identities. Whether you are a student seeking to excel in mathematics or a curious mind eager to uncover the secrets of algebraic manipulations, this video will captivate your imagination and ignite your passion for the beauty of mathematics.
Get ready to witness the magic of factorisation as we unveil the power of algebraic identities. Join us on this enchanting journey as we demystify complex expressions, unlock the hidden treasures of polynomials, and master the art of factorisation. Prepare to be spellbound by the elegance and effectiveness of algebraic identities, and let the magic of mathematics unfold before your eyes.
0:00 Intro
1:00 Important algebraic identities which is helpful for doing factorisarion
2:55 find the product(x+7)(x+5)
3:10 find the product(a-3)(a+ 6)
3:50 find the product(pq+5)(pq-5)
4:21 find the product(ab+cd)(ab+cd)
4:55 find the product (-z+3)(-z+a)
6:38 104\times96
6:44 53\times54
7:48 (102)^2
8:00 78\times82
8:40 Factorise using identity 9x^2+6xy+y^2
9:50 Factorise using identity 16y^2- 40ym + 25m^2
10:38 Factorise using identity 9a^2-\\frac{36}{121}b^2
11:30 (a+b+c)^2
11:45 (4a-2b+3c)^2
13:18 factorise 𝟒𝒙^𝟐+𝟗𝒚^𝟐+𝟏𝟔𝒛^𝟐+𝟏𝟐𝒙𝒚−𝟐𝟒𝒚𝒛−𝟏𝟔𝒙𝒛
15:12 Factorise 𝟐𝒙^𝟐+𝒚^𝟐+𝟖𝒛^𝟐−𝟐√𝟐 𝒙𝒚+𝟒√𝟐 𝒚𝒛−𝟖𝒙𝒛
17:11 Cubic Algebraic identities
18:10 Expansion of (𝟑𝒙−𝟒𝒚)^𝟑
19:30 Factorise 𝟖𝒙^𝟑+𝟐𝟕𝒚^𝟑+𝟑𝟔𝒙^𝟐 𝒚+𝟓𝟒𝒙𝒚^𝟐
20:35 a^3+b^3 and a^3-b^3
21:15 factorise 64x^3-125y^3
21:59 factorise 1000m^3-27m^3
22:20 x^3+y^3+z^3-3xyz
25:00 if x+y+z=0 thenx^3+y^3+z^3-=3xyz
25:40 Without actually expanding, find the values of the following (𝟏𝟎)^𝟑+(−𝟕)^𝟑+(−𝟑)^𝟑
26:24 Without actually expanding, find the values of the following (-8)^𝟑+(6)^𝟑+(2)^𝟑
27:05 Which of the following is a monomial having degree 82 ?(a) 𝒚^𝟖𝟐𝟎 (b) 𝟖𝟐𝟎𝒚 (c) 𝒙^𝟖𝟎𝟎 (d) 𝒎^𝟖𝟐
27:54 Find the value of the polynomial 𝟓𝒙−𝟒𝒙^𝟐+𝟑 𝒂𝒕 𝒙=−𝟏
28:42 If xy = 6 and 3x + 2y = 12, compute the value of 𝟗𝒙^𝟐+𝟒𝒚^𝟐
30:27 Zero of the polynomial 𝒑(𝒙)=𝟐𝒙+𝟓 is ________
30:54 If (x – 1) is a factor of 𝟒𝒙^𝟑+𝟑𝒙^𝟐−𝟒𝒙+𝒌, then find the value of k.
32:22 3 + 5 – 8 = 0. Then what is the value of (𝟑)^𝟑+(𝟓)^𝟑+(−𝟖)^𝟑
32:57 \frac{((𝟑𝟔𝟏)^𝟑 + (𝟏𝟑𝟗)^𝟑)}/{((𝟑𝟔𝟏)^𝟐 − 𝟑𝟔𝟏 \times 1𝟑𝟗 +(𝟏𝟑𝟗)^𝟐 )} is
34:40 𝒙+𝒚=𝟑, 𝒙^𝟐+𝒚^𝟐=𝟓. Find the value of xy.
35:44 If 𝐱−𝟏/𝐱=𝟒, evaluate 𝐱^𝟐+𝟏/𝐱^𝟐
36:40 If 𝐱^𝟐+𝟏/𝐱^𝟐 =𝟐𝟕, 𝐟𝐢𝐧𝐝 𝐱+𝟏/𝐱 𝐚𝐧𝐝 𝐱−𝟏/𝐱
Explore:
Follow us on :
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