Question

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1. simplify each expression \t10 pts

a) (9 - 2^4 + 10 ÷ 1) + 8
b) 3x^3y - 16xy + 5xy^3 + 2x^3y - 13xy + 4xy^3 + 2xy + 11xy^3 + x^3y

1. evaluate 5a^3 - 6a + 7a^2 - 8a^3 - 3a + 5a^2 - 12 + 11a + 4 when a = -1 \t10 pts

Explanation:

Step1: Simplify part a) exponents/parentheses

First, calculate exponents and inner parentheses: $2^3=8$, $0 \div 8=0$.
Expression: $(9 - 8) + 0 + 9$

Step2: Simplify part a) remaining operations

Solve parentheses, then add: $9-8=1$, $1+0+9=10$.
Expression: $1 + 0 + 9 = 10$

Step3: Simplify part b) group like terms

Group terms with $x^3y$, $x^2y$, $xy$, $xy^2$:
$(x^3y) + (3x^2y + 2x^2y) + (-16xy -13xy +2xy) + (5xy^2 +4xy^2 +11xy^2)$

Step4: Simplify part b) combine like terms

Calculate coefficients for each group:
$x^3y + 5x^2y -27xy +20xy^2$

Step5: Simplify question 2 group like terms

Group $a^3$, $a^2$, $a$, constants:
$(5a^3-8a^3)+(7a^2+5a^2)+(-6a-3a+11a)+(-12+4)$

Step6: Simplify question 2 combine like terms

Combine coefficients:
$-3a^3 +12a^2 +2a -8$

Step7: Evaluate question 2 at $a=-1$

Substitute $a=-1$ into the simplified expression:
$-3(-1)^3 +12(-1)^2 +2(-1) -8$

Step8: Calculate final value for question 2

Compute each term: $-3(-1)=3$, $12(1)=12$, $2(-1)=-2$. Sum: $3+12-2-8=5$
Expression: $3 + 12 - 2 - 8 = 5$

Answer:

1. a) $\boldsymbol{10}$

b) $\boldsymbol{x^3y + 5x^2y - 27xy + 20xy^2}$

1. $\boldsymbol{5}$