The multiplication or expansion of the algebraic expression (5x + 3)(5x - 3) is 25x² - 9. Hence, option C is the right choice.
What are the formulas required in the expansion of algebraic expressions?
Some of the formulas required in the expansion of algebraic expressions are as follows:
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- (a + b)(a - b) = a² - b²
- (a + b)² + (a - b)² = 2(a² + b²)
- (a + b)² - (a - b)² = 4ab
- (a + b)³ = a³ + 3a²b + 3ab² + b³
- (a - b)³ = a³ - 3a²b + 3ab² - b³
- a³ + b³ = (a + b)(a² - ab + b²)
- a³ - b³ = (a - b)(a² + ab + b²).
How to solve the question?
In the question, we are asked to multiply the algebraic expression (5x + 3)(5x - 3).
We know that the expression (5x + 3)(5x - 3) is of the form (a + b)(a - b).
The multiplication or the expansion of (a + b)(a - b) as we know, is a² - b².
Thus, the multiplication or the expansion of (5x + 3)(5x - 3) can be shown as:
(5x + 3)(5x - 3)
= (5x)² - (3)² {Since, (a + b)(a - b) = a² - b²}
= 25x² - 9.
Thus, the multiplication or expansion of the algebraic expression (5x + 3)(5x - 3) is 25x² - 9. Hence, option C is the right choice.
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