Answer:
(5x - 1)(5x - 1) = 25x² - 10x + 1
Step-by-step explanation:
Let us solve the question step by step
We need to find the product of (5x - 1) and (5x - 1)
- The first step multiply 1st term in 1st bracket by 1st term in 2nd bracket (5x by 5x)
∵ 5 × 5 = 25
∵ x × x = [tex]x^{1+1}[/tex] ⇒ multiply same base means add their powers
∴ x × x = x²
∴ 5x × 5x = 25x²
- The second step multiply 1st term in 1st bracket by 2nd term in 2nd bracket (5x by -1)
∵ 5x × -1 = (5 × -1)x
∴ 5x × -1 = -5x
- The third step multiply 2nd term in 1st bracket by 1st term in 2nd bracket (-1 by 5x)
∵ -1 × 5x = (-1 × 5)x
∴ -1 × 5x = -5x
- The fourth step multiply 2nd term in 2nd bracket by 2nd term in 2nd bracket (-1 by -1)
∵ -1 × -1 ⇒ (-)(-) = (+)
∴ -1 × -1 = 1
- The fifth step add them up
∵ (5x - 1)(5x - 1) = 25x² + -5x + -5x + 1
∵ -5x and -5x are like term, then add their coefficients
∵ -5x + -5x = (-5 + -5)x
∴ -5x + -5x = -10x
∴ (5x - 1)(5x - 1) = 25x² + -10x + 1
∵ (+)(-) = (-)
∴ (5x - 1)(5x - 1) = 25x² - 10x + 1
