please help
Simplify
Multiply
(2�ã7-4�ã2)(5�ã7+10�ã2)
Assuming your garbled symbol means √, we have
(2√7 - 4√2)(5√7 + 10√2)
just think of these as polynomials in x and y
(2x-4y)(5x+10y) = 10x^2 - 40y^2
letting x = √7 and y = √2, we have
10(√7)^2 - 40(√2)^2 = 10*7-40*2 = -10
Some work could have been saved by noting that
(2√7 - 4√2)(5√7 + 10√2)
= 2(√7-2√2) * 5(√7+√2)
= 10(√7-2√2)(√7+2√2)
= 10(7-8)
To simplify the given expression, we can use the FOIL method (First, Outer, Inner, Last) or the distributive property to multiply the two binomials.
Let's break down the steps to solve the problem:
Step 1: Distribute the first term of the first binomial (2�ã7) to both terms of the second binomial (5�ã7 and 10�ã2):
2�ã7 * 5�ã7 = 10�ã49
2�ã7 * 10�ã2 = 20�ã14
Step 2: Distribute the second term of the first binomial (-4�ã2) to both terms of the second binomial (5�ã7 and 10�ã2):
-4�ã2 * 5�ã7 = -20�ã14
-4�ã2 * 10�ã2 = -40�ã4
Step 3: Combine like terms obtained from the previous steps:
(10�ã49 + 20�ã14) + (-20�ã14 - 40�ã4)
Step 4: Simplify the expression further:
10�ã49 + 20�ã14 - 20�ã14 - 40�ã4
= 10�ã49 - 40�ã4
Thus, the simplified form of the expression (2�ã7-4�ã2)(5�ã7+10�ã2) is 10�ã49 - 40�ã4.
If you're interested in the step-by-step solution, using an online calculator or math software like Wolfram Alpha or Symbolab can be helpful.