Consider the above square figure whose side is a=(ab)+b units. (a +b)3= a3+b3+3a2b + 3ab2=a3+b3+3(ab)(a +b). Standard Identity-4: Algebraic identity for (x+a)(x+b) is: \((x + a)(x + b) = x^{2} + x(a + b) + ab\). Facebook page opens in new window Twitter page opens in new window Instagram page opens in new window YouTube page opens in new window Telegram page opens in new window Thus, we get 3 (1)2 + 4 = 7. Proof of \((a + b)^{2} = a^{2} + 2ab + b^{2}\). The App is absolutely free and can help you boost your preparations. In this method, you would need a prerequisite knowledge of Geometry, and some materials are needed to prove the identity." = 4 19 Once again, lets think of (a - b)2 as the area of a square with length (a - b). These can be related to factorization, trigonometry, integration and differentiation, quadratic equations, and more. So we have, (a - 2b) 3 = (a) 3 - (2b) 3 - 3(a)(2b)(a - 2b) = a . Standard Identity-1: Algebraic identity of the square of the summation of two terms is: Standard Identity-2: Algebraic identity of the square of the difference of two given terms is: Standard Identity-3: Algebraic identity of the difference of two squares is: \(a^2-b^2=\left(a+b\right)\left(a-b\right)\). Algebra gives all the possible methods for writing formulas and solving equations that are much clearer and easier than the writing everything in words as done earlier. CBSE Class 7 Mental Maths Algebraic Expression Worksheet www.studiestoday.com. Solution: To solve this, we need to use the following algebra identities: (a + b)2 + (a - b)2 = a2 + 2ab + b2 + a2 - 2ab + b2. The flower is the sexual reproduction organ. To understand this, let's begin with a large square of area a2. Factorize the following expression : \((x^4-1)\), \((x^4-1)\text{ can also be written as }((x^2)^2-1^2)\), Substituting a with \(x^2\) and b with 1, we get, Now, \((x^2-1)\) can be further factorized by using the same above identity by substituting a with x and b with 1. (x+5)(x+5)can also be written as\((x+5)^2\). Q5. Simplify the following expressions and then find the numerical values for x = -2. //