Take a = 7 and b = 3. Which statement is TRUE?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

(7 - 3)^{2} = 4^{2} = 16

, while

7^{2} - 3^{2} = 49 - 9 = 40

. So

a^{2} - b^{2}

is the larger value here. The two are different expressions —

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

— so they are not equal in general, and this single example is enough to disprove the last option.

Answer: C)

a^{2} - b^{2}

is greater than

(a - b)^{2}

Combine **like terms only** — same variables and same powers.

Example:

(3 x^{2} + 4 x - 2) + (5 x^{2} - 7 x + 8) = (3 x^{2} + 5 x^{2}) + (4 x - 7 x) + (- 2 + 8) = 8 x^{2} - 3 x + 6

.

For subtraction, distribute the minus sign first:

(3 x^{2} + 4 x) - (x^{2} - 2 x) = 3 x^{2} + 4 x - x^{2} + 2 x = 2 x^{2} + 6 x

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