Question

multiplying polynomials
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: Distribute $6v$ to each term

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

Step2: Distribute $7$ to each term

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

Step3: Distribute $2x$ to each term

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

Step4: Distribute $-4$ to each term

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

Step5: Use FOIL method

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

Step6: Use FOIL method

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

Step7: Use FOIL method

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

Step8: Use FOIL method

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

Step9: Use FOIL method

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

Step10: Use FOIL method

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

Step11: Use FOIL method

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

Step12: Use FOIL method

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

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. $25n^2 + 5n - 30$