Simplify the given algebraic expressions involving the variable t. For expression A, C, identify where t must…

Question

Simplify the given algebraic expressions involving the variable t. For expression A, C, identify where t must be multiplied into the brackets.

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the questions:

2.1.1 In which expressions must you multiply $t$ into the brackets?

The expressions where $t$ is multiplied into the brackets are A and C.

The expressions are $\boxed{A \text{ and } C}$ .

2.1.2 Simplify each expression.

A: $3 - t(t+5)$

Distribute $-t$ into the brackets.
$3 - t(t+5) = 3 - (t \cdot t + t \cdot 5) = 3 - (t^2 + 5t)$
Remove the brackets and simplify.
$3 - t^2 - 5t = \boxed{-t^2 - 5t + 3}$
B: $(t+3) - t$
Remove the brackets.
$t+3-t$
Combine like terms.
$t-t+3 = \boxed{3}$
C: $t(t+1)$
Distribute $t$ into the brackets.
$t(t+1) = t \cdot t + t \cdot 1 = \boxed{t^2 + t}$
D: $(t+1) + t+1$
Remove the brackets.
$t+1+t+1$
Combine like terms.
$t+t+1+1 = \boxed{2t+2}$
E: $(t+2) - 2t$
Remove the brackets.
$t+2-2t$
Combine like terms.
$t-2t+2 = \boxed{-t+2}$
F: $(t+2)(t-2)$
Apply the distributive property (FOIL method).
$(t+2)(t-2) = t(t-2) + 2(t-2) = t^2 - 2t + 2t - 4$
Combine like terms.
$t^2 - 2t + 2t - 4 = \boxed{t^2 - 4}$

Simplify the given algebraic expressions involving the variable t. For expression A, C, identify where t must be multiplied into the brackets.