Solve (a+?)(−2a+4) = −2a²−20a+48: Find the Missing Term

To solve the problem, we'll follow these steps:

• Step 1: Expand the expression $(a + ?)(-2a + 4)$ using the distributive property.
• Step 2: Equate the resulting expression with the given form $-2a^2 - 20a + 48$.
• Step 3: Solve for the missing '?' that satisfies the equation.

Step 1: Expand the original expression:

$(a + ?)(-2a + 4) = a(-2a) + a(4) + ?(-2a) + ?(4)$

Expanding gives us:

$-2a^2 + 4a - 2a? + 4?$

Step 2: Equate this with the provided expanded form $-2a^2 - 20a + 48$:

$-2a^2 + 4a - 2a? + 4? = -2a^2 - 20a + 48$

Step 3: Match the coefficients:

• Compare the linear terms $4a - 2a?$ with $-20a$:
• $4 - 2? = -20$ implies $4 = -20 + 2?$
• Solve for $?$:
• $2? = 24$ gives $? = 12$

The missing element is $12$.