Question

find each product.

1. $6v(2v + 3)$
2. $7(-5v - 8)$
3. $2x(-2x - 3)$
4. $-4(v + 1)$
5. $(2n + 2)(6n + 1)$
6. $(4n + 1)(2n + 6)$
7. $(x - 3)(6x - 2)$
8. $(8p - 2)(6p + 2)$
9. $(6p + 8)(5p - 8)$
10. $(3m - 1)(8m + 7)$
11. $(2a - 1)(8a - 5)$
12. $(5n + 6)(5n - 5)$

Explanation:

Step1: Apply distributive property

$6v(2v + 3) = 6v \cdot 2v + 6v \cdot 3$
$= 12v^2 + 18v$

Step2: Apply distributive property

$7(-5v - 8) = 7 \cdot (-5v) + 7 \cdot (-8)$
$= -35v - 56$

Step3: Apply distributive property

$2x(-2x - 3) = 2x \cdot (-2x) + 2x \cdot (-3)$
$= -4x^2 - 6x$

Step4: Apply distributive property

$-4(v + 1) = -4 \cdot v + (-4) \cdot 1$
$= -4v - 4$

Step5: Apply FOIL method

$(2n + 2)(6n + 1) = 2n \cdot 6n + 2n \cdot 1 + 2 \cdot 6n + 2 \cdot 1$
$= 12n^2 + 2n + 12n + 2$
$= 12n^2 + 14n + 2$

Step6: Apply FOIL method

$(4n + 1)(2n + 6) = 4n \cdot 2n + 4n \cdot 6 + 1 \cdot 2n + 1 \cdot 6$
$= 8n^2 + 24n + 2n + 6$
$= 8n^2 + 26n + 6$

Step7: Apply FOIL method

$(x - 3)(6x - 2) = x \cdot 6x + x \cdot (-2) + (-3) \cdot 6x + (-3) \cdot (-2)$
$= 6x^2 - 2x - 18x + 6$
$= 6x^2 - 20x + 6$

Step8: Apply FOIL method

$(8p - 2)(6p + 2) = 8p \cdot 6p + 8p \cdot 2 + (-2) \cdot 6p + (-2) \cdot 2$
$= 48p^2 + 16p - 12p - 4$
$= 48p^2 + 4p - 4$

Step9: Apply FOIL method

$(6p + 8)(5p - 8) = 6p \cdot 5p + 6p \cdot (-8) + 8 \cdot 5p + 8 \cdot (-8)$
$= 30p^2 - 48p + 40p - 64$
$= 30p^2 - 8p - 64$

Step10: Apply FOIL method

$(3m - 1)(8m + 7) = 3m \cdot 8m + 3m \cdot 7 + (-1) \cdot 8m + (-1) \cdot 7$
$= 24m^2 + 21m - 8m - 7$
$= 24m^2 + 13m - 7$

Step11: Apply FOIL method

$(2a - 1)(8a - 5) = 2a \cdot 8a + 2a \cdot (-5) + (-1) \cdot 8a + (-1) \cdot (-5)$
$= 16a^2 - 10a - 8a + 5$
$= 16a^2 - 18a + 5$

Step12: Apply FOIL method

$(5n + 6)(5n - 5) = 5n \cdot 5n + 5n \cdot (-5) + 6 \cdot 5n + 6 \cdot (-5)$
$= 25n^2 - 25n + 30n - 30$
$= 25n^2 + 5n - 30$

Answer:

1. $12v^2 + 18v$
2. $-35v - 56$
3. $-4x^2 - 6x$
4. $-4v - 4$
5. $12n^2 + 14n + 2$
6. $8n^2 + 26n + 6$
7. $6x^2 - 20x + 6$
8. $48p^2 + 4p - 4$
9. $30p^2 - 8p - 64$
10. $24m^2 + 13m - 7$
11. $16a^2 - 18a + 5$
12. $25n^2 + 5n - 30$