Answer:
(
t
+
w
)
4
=
t
4
+
4
t
3
w
1
+
6
t
2
w
2
+
4
t
1
w
3
+
w
4
Explanation:
First, you should get to know Pascal's triangle. Here's a small portion of it up to 6 lines. Basically you're just adding the numbers that are beside each other, then writing the sum below them. (For example,
1
+
2
in the third line equals to
3
in the fourth line.) If you want a better explanation for that, feel free to do some more research on it.
Expansion of ( 4- 2z)³ using binomial expansion is equals to
64 - 96z + 48z² - 8z³.
" Binomial theorem is a way of expanding a binomial expression with exponent n, where n is any positive integer."
Formula used
Binomial Expansion
(a - b) ⁿ = ⁿC₀ aⁿb⁰+ ⁿC₁ aⁿ⁻¹ (-b)¹ + ⁿC₂ aⁿ⁻² + ....... + (-1)ⁿ ⁿCₙ a° bⁿ
According to the question,
Given,
(4 -2z)³
a = 4
b = 2z
Substitute the value in the formula of binomial expansion we have,
= ³C₀ (4)³ (-2z)⁰ +³C₁ (4)² (-2z)¹ +³C₂ (4)¹ (-2z)² + ³C₃ (4)⁰ (-2z)³
= (4)³ - 3 (4)² (2z) + 3 (4) (2z)² -(2z)³
= 64 -96z +48z² -8z³
Hence, expansion of ( 4- 2z)³ using binomial expansion is equals to
64 - 96z + 48z² - 8z³.
Learn more about binomial theorem here
https://brainly.com/question/222308
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