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kuta software - infinite pre - algebra multiplying binomials find each …

Question

kuta software - infinite pre - algebra
multiplying binomials
find each product,

  1. (3n + 2)(n + 3)
  2. (n - 1)(2n - 2)
  3. (2x + 3)(2x - 3)
  4. (r + 1)(r - 3)
  5. (2n + 3)(2n + 1)
  6. (3p - 3)(p - 1)
  7. (3p + 3)(3p + 2)
  8. (k - 2)(k - 3)
  9. (v - 1)(3v - 3)
  10. (2x - 3)(3x + 3)
  11. (4n + 4)(5n - 8)
  12. (5x - 2)(5x - 8)
  13. (6x + 2)(2x + 8)
  14. (3x + 3)(x + 4)
  15. (5v + 4)(3v - 6)
  16. (x - 4)(x - 7)
  17. (5x + 6)(8x - 4)
  18. (8b - 1)(5b - 5)

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Explanation:

We use the FOIL method (First, Outer, Inner, Last) to multiply each pair of binomials: multiply the first terms, then outer terms, then inner terms, then last terms, then combine like terms.

Step1: Multiply (3n+2)(n+3)

First: $3n \times n = 3n^2$, Outer: $3n \times 3 = 9n$, Inner: $2 \times n = 2n$, Last: $2 \times 3 = 6$
Combine like terms: $3n^2 + 9n + 2n + 6 = 3n^2 + 11n + 6$

Step2: Multiply (n-1)(2n-2)

First: $n \times 2n = 2n^2$, Outer: $n \times (-2) = -2n$, Inner: $-1 \times 2n = -2n$, Last: $-1 \times (-2) = 2$
Combine like terms: $2n^2 - 2n - 2n + 2 = 2n^2 - 4n + 2$

Step3: Multiply (2x+3)(2x-3)

First: $2x \times 2x = 4x^2$, Outer: $2x \times (-3) = -6x$, Inner: $3 \times 2x = 6x$, Last: $3 \times (-3) = -9$
Combine like terms: $4x^2 - 6x + 6x - 9 = 4x^2 - 9$

Step4: Multiply (r+1)(r-3)

First: $r \times r = r^2$, Outer: $r \times (-3) = -3r$, Inner: $1 \times r = r$, Last: $1 \times (-3) = -3$
Combine like terms: $r^2 - 3r + r - 3 = r^2 - 2r - 3$

Step5: Multiply (2n+3)(2n+1)

First: $2n \times 2n = 4n^2$, Outer: $2n \times 1 = 2n$, Inner: $3 \times 2n = 6n$, Last: $3 \times 1 = 3$
Combine like terms: $4n^2 + 2n + 6n + 3 = 4n^2 + 8n + 3$

Step6: Multiply (3p-3)(p-1)

First: $3p \times p = 3p^2$, Outer: $3p \times (-1) = -3p$, Inner: $-3 \times p = -3p$, Last: $-3 \times (-1) = 3$
Combine like terms: $3p^2 - 3p - 3p + 3 = 3p^2 - 6p + 3$

Step7: Multiply (3p+3)(3p+2)

First: $3p \times 3p = 9p^2$, Outer: $3p \times 2 = 6p$, Inner: $3 \times 3p = 9p$, Last: $3 \times 2 = 6$
Combine like terms: $9p^2 + 6p + 9p + 6 = 9p^2 + 15p + 6$

Step8: Multiply (k-2)(k-3)

First: $k \times k = k^2$, Outer: $k \times (-3) = -3k$, Inner: $-2 \times k = -2k$, Last: $-2 \times (-3) = 6$
Combine like terms: $k^2 - 3k - 2k + 6 = k^2 - 5k + 6$

Step9: Multiply (v-1)(3v-3)

First: $v \times 3v = 3v^2$, Outer: $v \times (-3) = -3v$, Inner: $-1 \times 3v = -3v$, Last: $-1 \times (-3) = 3$
Combine like terms: $3v^2 - 3v - 3v + 3 = 3v^2 - 6v + 3$

Step10: Multiply (2x-3)(3x+3)

First: $2x \times 3x = 6x^2$, Outer: $2x \times 3 = 6x$, Inner: $-3 \times 3x = -9x$, Last: $-3 \times 3 = -9$
Combine like terms: $6x^2 + 6x - 9x - 9 = 6x^2 - 3x - 9$

Step11: Multiply (4n+4)(5n-8)

First: $4n \times 5n = 20n^2$, Outer: $4n \times (-8) = -32n$, Inner: $4 \times 5n = 20n$, Last: $4 \times (-8) = -32$
Combine like terms: $20n^2 - 32n + 20n - 32 = 20n^2 - 12n - 32$

Step12: Multiply (5x-2)(5x-8)

First: $5x \times 5x = 25x^2$, Outer: $5x \times (-8) = -40x$, Inner: $-2 \times 5x = -10x$, Last: $-2 \times (-8) = 16$
Combine like terms: $25x^2 - 40x - 10x + 16 = 25x^2 - 50x + 16$

Step13: Multiply (6x+2)(2x+8)

First: $6x \times 2x = 12x^2$, Outer: $6x \times 8 = 48x$, Inner: $2 \times 2x = 4x$, Last: $2 \times 8 = 16$
Combine like terms: $12x^2 + 48x + 4x + 16 = 12x^2 + 52x + 16$

Step14: Multiply (3x+3)(x+4)

First: $3x \times x = 3x^2$, Outer: $3x \times 4 = 12x$, Inner: $3 \times x = 3x$, Last: $3 \times 4 = 12$
Combine like terms: $3x^2 + 12x + 3x + 12 = 3x^2 + 15x + 12$

Step15: Multiply (5v+4)(3v-6)

First: $5v \times 3v = 15v^2$, Outer: $5v \times (-6) = -30v$, Inner: $4 \times 3v = 12v$, Last: $4 \times (-6) = -24$
Combine like terms: $15v^2 - 30v + 12v - 24 = 15v^2 - 18v - 24$

Step16: Multiply (x-4)(x-7)

First: $x \times x = x^2$, Outer: $x \times (-7) = -7x$, Inner: $-4 \times x = -4x$, Last: $-4 \times (-7) = 28$
Combine like terms: $x^2 - 7x - 4x + 28 = x^2 - 11x + 28$

Step17: Multiply (5x+6)(8x-4)

First: $5x \times 8x = 40x^2$, Outer: $5x \times (-4) = -20x$, Inner: $6 \times 8x = 48x$, Last: $6 \times (-4) =…

Answer:

  1. $3n^2 + 11n + 6$
  2. $2n^2 - 4n + 2$
  3. $4x^2 - 9$
  4. $r^2 - 2r - 3$
  5. $4n^2 + 8n + 3$
  6. $3p^2 - 6p + 3$
  7. $9p^2 + 15p + 6$
  8. $k^2 - 5k + 6$
  9. $3v^2 - 6v + 3$
  10. $6x^2 - 3x - 9$
  11. $20n^2 - 12n - 32$
  12. $25x^2 - 50x + 16$
  13. $12x^2 + 52x + 16$
  14. $3x^2 + 15x + 12$
  15. $15v^2 - 18v - 24$
  16. $x^2 - 11x + 28$
  17. $40x^2 + 28x - 24$
  18. $40b^2 - 45b + 5$