Question

practice: multiply two binomials
which of the following is equivalent to ((x + 3)(2x - 5)) ?
choose 1 answer:
a (x^2 - 2x - 15)
b (2x^2 - 2x - 15)
c (2x^2 + x - 15)
d (2x^2 + 6x - 5)
check
explain
practice: multiply two binomials with symbolic coefficients
((ax + 3)(bx + 2) = 9x^2 + 21x + 6)
in the equation above, (a) and (b) are constants. what is the value of (ab) ?
check

Explanation:

First Sub - Question (Multiplying \((x + 3)(2x - 5)\))

Step 1: Apply the distributive property (FOIL method)

Multiply the First terms: \(x\times2x = 2x^{2}\)
Multiply the Outer terms: \(x\times(-5)=-5x\)
Multiply the Inner terms: \(3\times2x = 6x\)
Multiply the Last terms: \(3\times(-5)=-15\)

Step 2: Combine like terms

Combine the middle terms: \(-5x+6x=x\)
So, \((x + 3)(2x - 5)=2x^{2}+x - 15\)

Second Sub - Question (\((ax + 3)(bx + 2)=9x^{2}+21x + 6\), find \(ab\))

Step 1: Apply the distributive property (FOIL method)

Multiply the First terms: \(ax\times bx=abx^{2}\)
Multiply the Outer terms: \(ax\times2 = 2ax\)
Multiply the Inner terms: \(3\times bx=3bx\)
Multiply the Last terms: \(3\times2 = 6\)

Step 2: Combine like terms for the \(x\) - terms

The \(x\) - terms are \(2ax+3bx=(2a + 3b)x\)
So, \((ax + 3)(bx + 2)=abx^{2}+(2a + 3b)x+6\)

Step 3: Equate coefficients

We know that \(abx^{2}+(2a + 3b)x + 6=9x^{2}+21x+6\)
Equating the coefficients of \(x^{2}\): \(ab = 9\) (since the coefficient of \(x^{2}\) on the right - hand side is 9)

Answer:

First sub - question: C. \(2x^{2}+x - 15\)
Second sub - question: 9