Question

1. $(2x - 1)(3x + 4)$
2. $(10 - x)(8 + x)$
3. $(- x + 21)(x + 2)$
4. indicate whether each number is rational or irrational.

0.45 $square$ rational $square$ irrational
$pi$ $square$ rational $square$ irrational
$sqrt{2}$ $square$ rational $square$ irrational
8.38383838... $square$ rational $square$ irrational
$\frac{4}{5}$ $square$ rational $square$ irrational

Explanation:

Step1: Expand using FOIL method

$(2x-1)(3x+4) = 2x\cdot3x + 2x\cdot4 -1\cdot3x -1\cdot4$

Step2: Simplify terms

$=6x^2 +8x -3x -4 = 6x^2+5x-4$

Step3: Expand using FOIL method

$(10-x)(8+x) = 10\cdot8 +10\cdot x -x\cdot8 -x\cdot x$

Step4: Simplify terms

$=80 +10x -8x -x^2 = -x^2+2x+80$

Step5: Expand using FOIL method

$(-x+21)(x+2) = -x\cdot x -x\cdot2 +21\cdot x +21\cdot2$

Step6: Simplify terms

$=-x^2 -2x +21x +42 = -x^2+19x+42$

Step7: Classify 8.38383838...

Repeating decimals are rational.

Step8: Classify $\frac{4}{5}$

Fractions are rational.

Answer:

1. $(2x-1)(3x+4) = 6x^2+5x-4$
2. $(10-x)(8+x) = -x^2+2x+80$
3. $(-x+21)(x+2) = -x^2+19x+42$
4. 8.38383838...: $\square$ rational $\square$ irrational (check rational)
5. $\frac{4}{5}$: $\square$ rational $\square$ irrational (check rational)