Question

kuta software - infinite algebra 1
multiplying polynomials
find each product.

1. 6x(2x + 3)
2. 7(-5y - 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)

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Explanation:

Step1: Distribute 6 to each term

$6v(2v+3)=6v\cdot2v + 6v\cdot3$
$=12v^2+18v$

Step2: Distribute 7 to each term

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

Step3: Distribute 2x to each term

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

Step4: Distribute -4 to each term

$-4(v+1)=-4\cdot v + (-4)\cdot1$
$=-4v-4$

Step5: Use FOIL method

$(2n+2)(6n+1)=2n\cdot6n + 2n\cdot1 + 2\cdot6n + 2\cdot1$
$=12n^2+2n+12n+2$
$=12n^2+14n+2$

Step6: Use FOIL method

$(4n+1)(2n+6)=4n\cdot2n + 4n\cdot6 + 1\cdot2n + 1\cdot6$
$=8n^2+24n+2n+6$
$=8n^2+26n+6$

Step7: Use FOIL method

$(x-3)(6x-2)=x\cdot6x + x\cdot(-2) + (-3)\cdot6x + (-3)\cdot(-2)$
$=6x^2-2x-18x+6$
$=6x^2-20x+6$

Step8: Use FOIL method

$(8p-2)(6p+2)=8p\cdot6p + 8p\cdot2 + (-2)\cdot6p + (-2)\cdot2$
$=48p^2+16p-12p-4$
$=48p^2+4p-4$

Step9: Use FOIL method

$(6p+8)(5p-8)=6p\cdot5p + 6p\cdot(-8) + 8\cdot5p + 8\cdot(-8)$
$=30p^2-48p+40p-64$
$=30p^2-8p-64$

Step10: Use FOIL method

$(3m-1)(8m+7)=3m\cdot8m + 3m\cdot7 + (-1)\cdot8m + (-1)\cdot7$
$=24m^2+21m-8m-7$
$=24m^2+13m-7$

Step11: Use FOIL method

$(2a-1)(8a-5)=2a\cdot8a + 2a\cdot(-5) + (-1)\cdot8a + (-1)\cdot(-5)$
$=16a^2-10a-8a+5$
$=16a^2-18a+5$

Step12: Use FOIL method

$(5n+6)(5n-5)=5n\cdot5n + 5n\cdot(-5) + 6\cdot5n + 6\cdot(-5)$
$=25n^2-25n+30n-30$
$=25n^2+5n-30$

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