PERKALIAN BENTUK ALJABAR

Calculate the result of 3x²(4xy).

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Answer explanation

To calculate 3x²(4xy), multiply the coefficients and combine like terms: 3 * 4 = 12, and x² * xy = x^(2+1) = x³. Thus, the result is 12x³y.

Simplify the algebraic expression (y + 2)(y - 3).

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Answer explanation

To simplify (y + 2)(y - 3), use the distributive property: y*y + y*(-3) + 2*y + 2*(-3) = y^2 - 3y + 2y - 6 = y^2 - y - 6. The simplified expression is y^2 - y - 6.

Simplify the algebraic expression (2x - 3)(x² + x - 5).

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Answer explanation

To simplify (2x - 3)(x² + x - 5), use the distributive property: multiply each term in the first expression by each term in the second. This results in 2x³ + 2x² - 10x - 3x² - 3x + 15, which simplifies to 2x³ - x² - 13x + 15.

What is the result of (a + 2)² - (α - 3)²?

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Answer explanation

The expression (a + 2)² - (α - 3)² can be simplified using the difference of squares formula: (x² - y² = (x - y)(x + y)). Here, x = (a + 2) and y = (α - 3). Thus, the result is ((a + 2) - (α - 3))((a + 2) + (α - 3)).

If a = 4x - 5 and b = 2x + 4, what is the result of a * b?

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Answer explanation

To find a * b, substitute a and b: (4x - 5)(2x + 4). Use the distributive property: 8x^2 + 16x - 10x - 20 = 8x^2 + 6x - 20. Thus, a * b = 8x^2 + 6x - 20.