Use an identity to evaluate 1.03 × 0.97.

0.9991. 1.03 × 0.97 = (1 + 0.03)(1 − 0.03) = 1² − (0.03)² = 1 − 0.0009 = 0.9991. Watch the square: (0.03)² = 0.0009, not 0.009 — that slip gives 0.991. The b² term is subtracted, so the answer sits just BELOW 1, ruling out 1.0009.

Use an identity to evaluate $1.03 \times 0.97$ .

Class 8Algebraic Expressions and IdentitiesAlgebra

A0.9991
B0.991
C1.0009
D0.97

Step-by-Step Solution

1.03 \times 0.97 = (1 + 0.03) (1 - 0.03) = 1^{2} - (0.03)^{2} = 1 - 0.0009 = 0.9991

. Watch the square:

(0.03)^{2} = 0.0009

, not 0.009 — that slip gives 0.991. The

b^{2}

term is subtracted, so the answer sits just BELOW 1, ruling out 1.0009.

Answer: A) 0.9991

Key idea: The three classic identities

Three identities you will use forever:

**1.

(a + b)^{2} = a^{2} + 2 ab + b^{2}

**
Example:

(x + 5)^{2} = x^{2} + 10 x + 25. * * 2. (a - b)^{2} = a^{2} - 2 ab + b^{2}

**
Example:

(3 x - 2)^{2} = 9 x^{2} - 12 x + 4. * * 3. (a + b) (a - b) = a^{2} - b^{2}

** (difference of squares)
Example:

(x + 7) (x - 7) = x^{2} - 49

.

All three can be derived by FOIL — but memorising them lets you skip steps and spot patterns.

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Don't just memorise the answer — build a daily practice habit.

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Use an identity to evaluate 1.03×0.97.

Step-by-Step Solution

Key idea: The three classic identities

Master this chapter in 30 minutes a day.

More Class 8 Algebraic Expressions and Identities practice

Use an identity to evaluate $1.03 \times 0.97$ .