Answer:
309
Step-by-step explanation:
(2x-)^5
step 1
1 5 10 10 5 1
step 2
1(2x¹-3^0) 5(2x²-3^5) 10(2x³-3^4)
10(2x^4-3³) 5(2x^5-3²)
1(2x^0-3¹)
step 3
(2x) (10x²-243) (20x³-81) (20x^4-27)
(10x^5-9) (2-3)
step 4
2 -243-61-7 +1 -1=309
The coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720
The correct answer is an option (E)
"It refers to a number or quantity placed with a variable."
"The alphabetic character that expresses a numerical value."
"It is a mathematical expression which consists of numbers, variables and mathematical operations."
" [tex](a-b)^3=a^3-3a^2b+3ab^2- b^3[/tex] "
" [tex](a-b)^2=a^2-2ab+b^2[/tex] "
For given question,
We have been given an expression [tex](2x-3)^5[/tex]
We need to expand given expression.
[tex](2x-3)^5\\\\= (2x-3)^3\times (2x-3)^2\\\\=[(2x)^3-3(2x)^23+3(2x)(3)^2- 3^3]\times ((2x)^2-2(2x)(3)+3^2)\\\\=[8x^3-36x^2+54x-27]\times [4x^2-12x+9]\\\\=-243+810x-1080x^2 +720x^3-240x^4+32x^5\\\\=32x^5-240x^4+720x^3-1080x^2+810x-243[/tex]
Therefore, the coefficient of [tex]x^3[/tex] in the expansion of [tex](2x-3)^5[/tex] is 720
The correct answer is an option (E)
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