Mathematics is like music – Enjoy it!!!
Example 24: Factorise 8×3 + 27y3 + 36x2y + 54xy2 Example 23 Example 25 Prerequisite You must be aware of the identity: (x + y)3 = x3 + y3 + 3xy (x + y). if you feel that you cannot…
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Rational root theorem: Given a polynomial P(x) = anxn + an-1xn-1 + …… + a1x + a0 with integral coefficients, an≠0. If has a rational root p/q with p & q relatively prime positive integers, then p is a divisor of…
Read MoreExample 23: Evaluate each of the following using suitable identities: (i) (104)3 (ii) (999)3 Example 22 Example 24 Prerequisite Not a big deal for anyone. Split these in (100 + 4) and (1000 – 1) and then find the cube…
Read MoreExample 22: Write the following cubes in the expanded form: (i) (3a + 4b)3 (ii) (5p – 3q)3 Example 21 Example 23 Prerequisite Easy!!! If you know the trick to write these identities quickly using pascal’s triangle, you will save…
Read MoreExample 21: Factorise 4×2 + y2 + z2 – 4xy – 2yz + 4xz. Example 20 Example 22 Prerequisite Negetive terms in the middle does not make any difference and we will use the same identity that we used in…
Read MoreExample 20: Expand (4a – 2b – 3c)2. Example 19 Example 21 Prerequisite It is exact copy of previous question. the negative terms does not make any difference. This question can also be written as (4a + (-2b) + (-3c)).…
Read MoreExample 19: Write (3a + 4b + 5c)2 in expanded form. Example 18 Example 20 Prerequisite This seems bit tricky and difficult identity to remember but you need not pressurise yourself to remember the expanded form of such identities. You…
Read MoreExample 18: Factorise: (i) 49a2 + 70ab + 25b2 (ii) 24/4 x2 – y2 / 9 Example 17 Example 19 Prerequisite The most common algebraic identities are used to solve this question. Learn how to quickly write expanded form of these…
Read MoreExample 17: Evaluate 105 × 106 without multiplying directly. Example 16 Example 18 Prerequisite As mentioned in the previous question, you must understand and remember few very important algebraic identities. Algebraic Identities
Read MoreExample 16: Find the following products using appropriate identities: (i) (x + 3) (x + 3) (ii) (x – 3) (x + 5) Example 15 Example 17 Prerequisite Extremely important for every student to learn and remember few algebraic identities.…
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