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Class 8 We Distribute, Yet Things Multiply: cheat sheet
CBSE Mathematics. The distributive property turns products into sums. Four identities follow from it and make squaring and multiplying quick.
Key ideas
- Distributive property: a(b + c) = ab + ac, and (a + b)(c + d) = ac + ad + bc + bd.
- An identity is true for every value of the letters.
- A square of a sum or difference has three terms, not two.
- Quick squares: 99² = (100 − 1)² = 10 000 − 200 + 1 = 9801.
- Quick products: 52 × 48 = (50 + 2)(50 − 2) = 2500 − 4 = 2496.
- Areas show the identities: a square of side a + b splits into a², b² and two rectangles ab.
Remember
| Square of a sum | (a + b)² = a² + 2ab + b² |
| Square of a difference | (a − b)² = a² − 2ab + b² |
| Sum times difference | (a + b)(a − b) = a² − b² |
| Two binomials | (x + a)(x + b) = x² + (a + b)x + ab |
Watch out
- Writing (a + b)² = a² + b², leaving out 2ab.
- Getting the sign of the middle term wrong in (a − b)².
- Multiplying only the first terms of each bracket.
Worked example
A rectangle 13 m by 11 m has both its length and breadth increased by 4 m. By how much does its area increase?
Working: (13 + 4)(11 + 4) − 13 × 11 = 4(13 + 11) + 4²
Answer: 112 m²
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