● The following identities are proved geometrically:
* (x + a)(x +b) = x 2 + x(a + b) +ab
* (a + b)2 =a2 + 2ab +b2
* (a − b)2 =a2 − 2ab +b2 and
* (a +b)(a − b) = a 2 −b2 .
● The factors of an algebraic expression is two or more expressions whose product is the given expression.
● The process of writing an algebraic expression as the product of its factors is called factorisation.
● An algebraic statement that shows two algebraic expression being unequal is known as an algebraic inequation.
● The algebraic expressions are connected with any one of the four signs of inequalities, namely, >, ≥ ,< and ≤.
● When both sides of an inequation are added, subtracted, multiplied and divided by the same non-zero positive number, the inequality remains the same.
● When both sides of an inequation are multiplied or divided by the same non-zero negative number, the sign of inequality is reversed. For example, x < y ⇒ −x >−y .
● The solutions of an inequation can be represented on the number line by marking the true values of solutions with different colour on the number line.
Step – 1
Open the Browser and type the URL Link given below (or) Scan the QR Code. GeoGebra work sheet named “(x+a)(x+b)” will open. Drag the sliders to change x, a, b values. Check the steps on right side.
Step - 2
After completing Click on “Inequation” in the left side. Move the slider below to change “a” value.Click on the check boxes to see respective inequations on the number line.
Browse in the link
(x+a)(x+b): https://www.geogebra.org/m/f4w7csup#material/nguv3yey or Scan the QR Code.