Question

Which expression is equivalent to

`\left(x-5\right)\left(2x+3\right)` ?..

Answer 1

Which expression is equivalent to



`\left(\frac{1}{2}a+5\right)\left(\frac{3}{2}a+1\right)` ?

Answer 2

To find an expression equivalent to \((x - 5)(2x + 3)\), we can use the distributive property (also known as the FOIL method for binomials). Let's expand the expression step by step:

1. Distribute \(x\) over \(2x + 3\):
\[
x \cdot (2x) + x \cdot (3) = 2x^2 + 3x
\]

2. Distribute \(-5\) over \(2x + 3\):
\[
-5 \cdot (2x) + (-5) \cdot (3) = -10x - 15
\]

3. Now, combine the results from steps 1 and 2:
\[
2x^2 + 3x - 10x - 15
\]

4. Combine like terms:
\[
2x^2 + (3x - 10x) - 15 = 2x^2 - 7x - 15
\]

Thus, the expression equivalent to \((x - 5)(2x + 3)\) is:
\[
\boxed{2x^2 - 7x - 15}
\]

Answer 3

To find an expression equivalent to \(\left(\frac{1}{2}a + 5\right)\left(\frac{3}{2}a + 1\right)\), we can use the distributive property (or the FOIL method). Let's expand the expression step by step:

1. Distribute \(\frac{1}{2}a\) over \(\frac{3}{2}a + 1\):
\[
\frac{1}{2}a \cdot \left(\frac{3}{2}a\right) + \frac{1}{2}a \cdot 1 = \frac{3}{4}a^2 + \frac{1}{2}a
\]

2. Distribute \(5\) over \(\frac{3}{2}a + 1\):
\[
5 \cdot \left(\frac{3}{2}a\right) + 5 \cdot 1 = \frac{15}{2}a + 5
\]

3. Now, combine the results from steps 1 and 2:
\[
\frac{3}{4}a^2 + \frac{1}{2}a + \frac{15}{2}a + 5
\]

4. Combine the like terms:
\[
\frac{3}{4}a^2 + \left(\frac{1}{2}a + \frac{15}{2}a\right) + 5 = \frac{3}{4}a^2 + \frac{16}{2}a + 5 = \frac{3}{4}a^2 + 8a + 5
\]

Thus, the expression equivalent to \(\left(\frac{1}{2}a + 5\right)\left(\frac{3}{2}a + 1\right)\) is:
\[
\boxed{\frac{3}{4}a^2 + 8a + 5}
\]