Evaluate 78² − 22² without doing any long multiplication.

Evaluate $7 8^{2} - 2 2^{2}$ without doing any long multiplication.

Class 8Algebraic Expressions and IdentitiesAlgebra

7 8^{2} - 2 2^{2} = (78 + 22) (78 - 22) = 100 \times 56 = 5600

. The identity turns the difference of squares into the SUM times the DIFFERENCE. Squaring the difference instead gives

5 6^{2} = 3136

, and stopping at the difference gives 56.

Answer: C) 5600

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.

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