Factorise a2 + b2 + 2 ab + bc + ca
WebFeb 24, 2024 · Example 6: If a + b + c = 18 and a 2 + b 2 + c 2 = 116 calculate the value of ab + bc + ca. Given. a + b + c = 18. a2 + b2 + c2 = 116. Formula\Concept used (a + b + c) 2 = a2 + b2 + c2 + 2(ab + bc + ca) Calculation. Clearly, 18 2 = 116 + 2(ab + bc + ca) 2(ab + bc + ca) = 208. ab + bc + ca = 104 WebThe a^2 + b^2 formula is used to calculate the sum of two or more squares in an expression. Thus, a sum of squares formula or a^2 + b^2 formula can be expressed as: a 2 + b 2 = (a +b) 2 - 2ab. Also, a 2 + b 2 = (a - b) 2 + 2ab. where, a, b = arbitrary numbers. Let a and b be the two numbers, the squares of a and b are a 2 and b 2.
Factorise a2 + b2 + 2 ab + bc + ca
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WebMay 21, 2024 · A^2 + b^2 + 2(ab+bc+ca) = a^2 + b^2 + c^2 +2ab + 2bc +2ac -c^2 = (a+b+c)^2 - c^2 = (a+b+2c)(a+b) this means m=0 and n=2 so m+n= 0+2 = 2 Advertisement Advertisement Nomitha Nomitha After factorization the factors are (a+b)(a+b+2c) so m=0, n=2 m+n=2 yeah I missed 2 while factorization tnx for ur correction WebFeb 1, 2015 · $$ (a+b+c)^2 = a^2 + b^2 +c^2 + 2(ab + bc + ca) $$ The LHS of the above identity is a perfect square, hence it is always positive or 0. Thus, $$ a^2 + b^2 +c^2 + 2(ab + bc + ca) ≥ 0 $$
WebJun 10, 2024 · factorise a^2+b^2-2(ab-ac+bc). factorise 4a^2-9b^2-(2a-3b). factorise a-b-a2+b2. factorise 108a^2-3(b-c)^2. factorise 25x^2-10x+1-36y^2#polynomialsbyavisir #... WebApr 3, 2024 · A^2 + b^2 - 2(ab - ac +bc) = a^2 + b^2 - 2ab + 2ac - 2bc = (a- b)^2 + 2ac - 2bc [ we know that a^2 + b^2 - 2ab = (a-b)^2] = (a- b)^2 +2c (a-b) = (a- b) (a-b + 2c) Hope it helps..
Webab (a 2 + b 2 - c 2) - bc (c 2 - a 2 - b 2) + ca (a 2 + b 2 - c 2) = ab (a 2 + b 2 - c 2) + bc (a 2 + b 2 - c 2) + ca (a 2 + b 2 - c 2) = (a 2 + b 2 - c 2 ) [ab + bc + ca] Concept: Factorisation by Taking Out Common Factors Is there an error in this question or solution? Chapter 5: Factorisation - Exercise 5 (A) [Page 68] Q 3 Q 2 Q 4 WebExamples on a2 + b2 + c2 Formula. Let us take a look at a few examples to better understand the formula of a 2 + b 2 + c 2. Example 1: Find the value of a 2 + b 2 + c 2 if a + b + c = 10 and ab + bc + ca = -2. Solution: To find: a 2 + b 2 + c 2 Given that: a + b + c = 10 ab + bc + ca = -2 Using the a 2 + b 2 + c 2 formula,
WebClick here👆to get an answer to your question ️ Factorise a^2 + b^2 + 2(ab + bc + ca) Solve Study Textbooks Guides. Join / Login. Question . Factorise a 2 + b 2 + 2 (a b + b c + c a) A (a + b) (a + b + 2 c) B (b + c) (c + a + 2 b) C (c + a) (a + b + 2 c) D (b + a) (b + c + 2 a) Medium. Open in App. ... If a + b + c = 1 0 and a 2 + b 2 + c 2 ...
WebApr 29, 2024 · Which of the following are the factors of a2 + ab +bc + ca [ ] A) (b + c) (c + a) B) (a + b) (a + c) C) a (a + b + c) D) (a + b) (b + c). Advertisement Answer 11 people … openstax pdf download historyWebQ. Factorise a 2 + b 2 + 2 (a b + b c + c a) Q. Factorise the expression a 2 − a b − a c + b c : Q. Factorise: a 2 + b 2 4 + c 2 9 − a b + b c 3 − 2 3 c a openstax organizational behavior citationWebFactorise b² + c² + 2 (ab + bc + ca) Mathematics For Class 9 - YouTube 0:00 / 17:19 Factorise b² + c² + 2 (ab + bc + ca) Mathematics For Class 9 Sagar Jha Classes 4... openstax.org biology 2eWebIf a+ b+ c = 0 and a2 + b2 + c2 = ab +bc +ac, then it follows that 0 = (a+ b+ c)2 = a2 +b2 +c2 +2(ab+ bc +ac), or a2 +b2 +c2 = −2(ab +bc +ac). Put this together and we will see that in fact a2 + b2 + c2 = 0, ... Infinite expansion of non … ip camera occupation detectionWebJun 28, 2016 · Prove that $$ \begin{vmatrix} 1 & a^2 + bc & a^3 \\ 1 & b^2 + ac & b^3 \\ 1 & c^2 + ab & c^3 \\ \end{vmatrix} =(a-b)(b-c)(c-a)(a^... Stack Exchange Network Stack Exchange network consists of 181 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build … openstax physics 1 textbookWebIdentity 1: (a+b) 2 = a 2 + b 2 + 2ab Identity 2: (a-b) 2 = a 2 + b 2 – 2ab Identity 3: a 2 – b 2 = (a+b) (a-b) What is the difference between an algebraic expression and identities? An algebraic expression is an expression which consists of variables and constants. In expressions, a variable can take any value. openstax precalculus answer keyWebHow to factor this a^2(b-c) +b^2(c-a) +c^2(a-b) - Quora Answer (1 of 4): This is a classic. = a^2b - a^2c + b^2c - b^2a + c^2a-c^2b =a^2b - b^2a - a^2c + b^2c + c^2a -c^2b = ab(a - b) - c(a^2 - b^2) +c^2(a - b) =ab(a - b) -c(a - b)(a + b) +c^2(a - b) =(a - b)(ab - c(a + b) +c^2) =(a - b)(ab - cb -ca + c^2) = ... openstax physics 2 answers