Question

Sample Work Help Needed! Please answer these questions and show the steps used to solve them. NO DECIMAL ANSWERS (except on three)

Simplify.
1. (-2x3y4)(5x9y-2)

Simplify. Write in Scientific Notation
2. 8(32 x 1011)

Multiply.
3. (3x – 1)(5x + 4)

Factor.
4. 8x2 + 2x - 3

Answer 1

1. Using the exponent rule (a^b)·(a^c) = a^(b+c) ...

`\left(-2x^3y^4\right)\left(5x^9y^(-2)\right)=(-2)(5)\left(x^((3+9))y^((4-2))\right)\\\\=-10x^(12)y^(2)`

Simplify. Write in Scientific Notation

2. You know that 256 = 2.56·100 = 2.56·10². After that, we use the same rule for exponents as above.

`8 \left(32* 10^(11)\right)=(8)(32)* 10^(11)=256* 10^(11)=2.56* 10^(13)`

3. The distributive property is useful for this.

(3x – 1)(5x + 4) = (3x)(5x + 4) – 1(5x + 4)

... = 15x² +12x – 5x –4

... = 15x² +7x -4

4. Look for factors of 8·(-3) = -24 that add to give 2, the x-coefficient.

-24 = -1×24 = -2×12 = -3×8 = -4×6

The last pair of factors adds to give 2. Now we can write

... (8x -4)(8x +6)/8 . . . . . where each of the instances of 8 is an instance of the coefficient of x² in the original expression. Factoring 4 from the first factor and 2 from the second factor gives

... (2x -1)(4x +3) . . . . . the factorization you require