Subtract algebraic expressions, including polynomials. Solve addition and subtraction problems involving…

Question

Subtract algebraic expressions, including polynomials. Solve addition and subtraction problems involving polynomials.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the subtraction problems.

Write the subtraction expression.
$(6a - 2b - 4c) - (10a - 4b)$
Distribute the negative sign.
$6a - 2b - 4c - 10a + 4b$
Group like terms.
$(6a - 10a) + (-2b + 4b) - 4c$
Combine like terms.
$-4a + 2b - 4c$
The result is $\boxed{-4a + 2b - 4c}$ .
1. Subtract $4a^2 + b^2 + 4c^2$ from the sum of $2a^2 + 3b^2 - 4c^2$ and $6a^2 - 2b^2 + 3c^2$ .
Find the sum of $2a^2 + 3b^2 - 4c^2$ and $6a^2 - 2b^2 + 3c^2$ .
$(2a^2 + 3b^2 - 4c^2) + (6a^2 - 2b^2 + 3c^2)$ $= (2a^2 + 6a^2) + (3b^2 - 2b^2) + (-4c^2 + 3c^2)$ $= 8a^2 + b^2 - c^2$
Subtract $4a^2 + b^2 + 4c^2$ from the sum found in Step 1.
$(8a^2 + b^2 - c^2) - (4a^2 + b^2 + 4c^2)$
Distribute the negative sign.
$8a^2 + b^2 - c^2 - 4a^2 - b^2 - 4c^2$
Group like terms.
$(8a^2 - 4a^2) + (b^2 - b^2) + (-c^2 - 4c^2)$
Combine like terms.
$4a^2 + 0 - 5c^2$ $4a^2 - 5c^2$
The result is $\boxed{4a^2 - 5c^2}$ .

Subtract algebraic expressions, including polynomials. Solve addition and subtraction problems involving polynomials.