Question

(2x + 5) (4x − 3) (5x - 4) can be expanded and fully simplified to give an expression of the form ax³ + bx² + cx + d.

Work out the values of a, b, c and d.

Answer 1

To find the values of a, b, c, and d in the expanded form ax³ + bx² + cx + d, expand the expression (2x + 5) (4x − 3) (5x - 4) by multiplying the binomials step by step, and then combine like terms. The final simplified form reveals the coefficients of the expression as a=8, b=7.6, c=8.8, and d=-60.

Step-by-step explanation:

To expand and simplify the expression (2x + 5) (4x − 3) (5x - 4) into the form ax³ + bx² + cx + d, we first need to multiply the first two binomials before multiplying the result by the third binomial.

Step 1: Multiply (2x + 5) and (4x - 3) to get the intermediate product.
8x² - 6x + 20x - 15 = 8x² + 14x - 15

Step 2: Now take this intermediate product and multiply it by the third binomial (5x - 4).
8x³ - 6.4x² + 14x²x - 11.2x + 20x - 15x - 60 = 8x³ + (14x - 6.4) x² + (20x - 11.2x - 15) + (- 60).

Step 3: Combine like terms to get the fully simplified form.
8x³ + 7.6x² + (8.8x - 15) - 60

Therefore, the values for a, b, c, and d in the expression ax³ + bx² + cx + d are a=8, b=7.6, c=8.8, and d=-60.

Answer 2

To expand (2x + 5) (4x − 3) (5x - 4), you can use the distributive property and the FOIL method.

The distributive property states that for any two algebraic expressions a and b, and for any two numbers x and y, (a+b)(x+y) = ax + ay + bx + by.

The FOIL method is a way to multiply two binomials. It stands for First, Outside, Inside, Last, and it involves multiplying the first term of the first binomial by the first term of the second binomial, the first term of the first binomial by the second term of the second binomial, the second term of the first binomial by the first term of the second binomial, and the second term of the first binomial by the second term of the second binomial.

Using these methods, you can expand (2x + 5) (4x − 3) (5x - 4) as follows:

(2x + 5) (4x − 3) (5x - 4) = (2x)(4x)(5x) + (2x)(4x)(-4) + (2x)(-3)(5x) + (2x)(-3)(-4) + (5)(4x)(5x) + (5)(4x)(-4) + (5)(-3)(5x) + (5)(-3)(-4)

This can be simplified to:

= 40x³ - 32x² - 60x³ + 48x² - 20x³ + 15x² + 60x - 20x + 100x² - 20x + 12

Combining like terms, we get:

= -12x³ + 143x² + 100x + 12

So, the values of a, b, c, and d are a = -12, b = 143, c = 100, and d = 12.

Step-by-step explanation: