Identify the constant term in algebraic expressions and simplify algebraic expressions.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to your algebra problems.

1. Write down the constant term in each of these expressions:

1.a) $6x^2 - 10xy + 5 - 7y^3$ The constant term is the term without any variables. The constant term is $\boxed{5}$ .
1.b) $12 + 4abc - 2ba + 13cd$ The constant term is the term without any variables. The constant term is $\boxed{12}$ .
1.c) $24m^3 + 12mn^3 - 33 - 60m^3$ The constant term is the term without any variables. The constant term is $\boxed{-33}$ .

2. Simplify where possible:

2.a) $x^2 + y^2$ These are not like terms, so the expression cannot be simplified further. The simplified expression is $\boxed{x^2 + y^2}$ .
2.b) $3y^2 - 10y^2$

Combine the coefficients of the like terms ( $y^2$ ).
$$ (3 - 10)y^2 $$
Perform the subtraction.
$$ -7y^2 $$ The simplified expression is $\boxed{-7y^2}$.
- 2.c) $2x^2 + 9x - x^2 + 12x$
Group like terms.
$$ (2x^2 - x^2) + (9x + 12x) $$
Combine the coefficients of the like terms.
$$ (2 - 1)x^2 + (9 + 12)x $$
Perform the operations.
$$ x^2 + 21x $$ The simplified expression is $\boxed{x^2 + 21x}$.
- 2.d) $15ab + ab$
Combine the coefficients of the like terms ( $ab$ ).
Remember $ab$ is $1ab$ . $(15 + 1)ab$
Perform the addition.
$$ 16ab $$ The simplified expression is $\boxed{16ab}$.
- 2.e) $3ab + 4b - 6b - 7ab + 5c$
Group like terms.
$$ (3ab - 7ab) + (4b - 6b) + 5c $$
Combine the coefficients of the like terms.
$$ (3 - 7)ab + (4 - 6)b + 5c $$
Perform the operations.
$$ -4ab - 2b + 5c $$ The simplified expression is $\boxed{-4ab - 2b + 5c}$.
- 2.f) $10x^2y^3 - 5x^2y^3$
Combine the coefficients of the like terms ( $x^2y^3$ ).
$$ (10 - 5)x^2y^3 $$

$$
5x^2y^3
$$
The simplified expression is $\boxed{5x^2y^3}$.

Step-by-step solution