The expansion of (2x - 3y)⁴ is a polynomial with the sum of multiple terms, each of them with different degrees and coefficients. The term of a polynomial refers to each element of the polynomial, it can be a constant, a variable with a coefficient, or a combination of variables with coefficients.
To find the terms of the expansion of (2x - 3y)⁴, we can use the binomial theorem:
Jawab:
Penjelasan dengan langkah-langkah:
The expansion of (2x - 3y)⁴ is a polynomial with the sum of multiple terms, each of them with different degrees and coefficients. The term of a polynomial refers to each element of the polynomial, it can be a constant, a variable with a coefficient, or a combination of variables with coefficients.
To find the terms of the expansion of (2x - 3y)⁴, we can use the binomial theorem:
(2x - 3y)⁴ = (2x - 3y)(2x - 3y)(2x - 3y)(2x - 3y)
= (2x)⁴ - 4(2x)³(3y) + 6(2x)²(3y)² - 4(2x)(3y)³ + (3y)⁴
So the terms in the expansion of (2x - 3y)⁴ are:
(2x)⁴ = 16x⁴
-4(2x)³(3y) = -48x³y
6(2x)²(3y)² = 216x²y²
-4(2x)(3y)³ = -144xy³
(3y)⁴ = 81y⁴
So the expansion of (2x - 3y)⁴ is :
(2x - 3y)⁴ = 16x⁴ - 48x³y + 216x²y² - 144xy³ + 81y⁴