Page 110 - Start Up Mathematics_8 (Non CCE)

Note: WI = x + a and WP = x; \ PI = WI – WP = x + a – x = a
Similarly, IN = x + b and IQ = x
\ QN = IN – IQ = x + b – x = b.
Step 2: Through P draw PR parallel to WG, meeting GN at R.
Step 3: Through Q draw QS parallel to WI, meeting GW at S. Mark the point of intersection of PR and
QS as O.

Step 4: Paste this cardboard on a sheet of paper and colour the different regions.

Note: The rectangle is divided into 4 regions.
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I. Square WPOS with side x cm and area = x cm 2
II. Rectangle PIQO with dimensions x cm ¥ a cm and area = ax cm 2
III. Rectangle OQNR with dimensions a cm ¥ b cm and area = ab cm 2
IV. Rectangle SORG with dimensions x cm ¥ b cm and area = bx cm 2
Total area of rectangle WING = Area I + Area II + Area III + Area IV
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(x + a)(x + b) = x + ax + ab + bx = x + ax + bx + ab = x + (a + b)x + ab
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Hence, (x + a)(x + b) = x + (a + b)x + ab.
AT a Glance

1. An algebraic expression is a phrase with one or more algebraic terms. It is a combination of constants
and variables connected by fundamental operations i.e., +, –, ¥ and ÷ .
2. In an algebraic expression, the elements separated by the ‘+’ or ‘–’ sign are called terms.
3. The number part of the terms with variables are called coefficients.
4. Terms with identical symbolic variables are called like terms and the others unlike terms.
5. Algebraic expressions where variables have non-negative integral powers with one term are monomials,
with two terms are binomials and with three terms are trinomials.
6. In addition or subtraction of algebraic expressions, like terms are grouped and the sum or difference of
each group is found out.

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