Question

algebra 1
name
assignment
date______ per
find each product.

1. $(3r + 8)(5r + 4)$
2. $(2x - 1)(5x + 1)$
3. $(4n + 8)(n - 1)$
4. $(n + 7)(n + 3)$
5. $(2x + 1)(6x - 5)$
6. $(4n - 3)(n - 1)$
7. $(7m - 8)(m - 6)$
8. $(8x + 8)(3x + 7)$
9. $(4n + 1)(2n - 1)$
10. $(6p - 5)(2p - 8)$
11. $(p + 7)(3p - 6)$
12. $(3x - 3)^2$
13. $(3x + 2)(3x - 7)$
14. $(7b + 3)(2b + 4)$
15. $(3k - 7)(4k + 6)$
16. $(4r + 5)(3r - 3)$
17. $(7x - 8)(4x - 3)$
18. $(8r - 7)(3r - 8)$
19. $(x + 8)(5x - 1)$
20. $(7x - 2)(4x + 4)$
21. $(x + 1)(3x - 1)$
22. $(8m - 3)^2$
23. $(b + 6)(b - 6)$
24. $(6x - 4)(7x - 7)$

Explanation:

Step1: Apply FOIL method

$(a+b)(c+d)=ac+ad+bc+bd$
---

1) $(3r+8)(5r+4)$

Step1: Multiply first terms

$3r \times 5r = 15r^2$

Step2: Multiply outer terms

$3r \times 4 = 12r$

Step3: Multiply inner terms

$8 \times 5r = 40r$

Step4: Multiply last terms

$8 \times 4 = 32$

Step5: Combine like terms

$15r^2 + 12r + 40r + 32 = 15r^2 + 52r + 32$

2) $(2x-1)(5x+1)$

Step1: Multiply first terms

$2x \times 5x = 10x^2$

Step2: Multiply outer terms

$2x \times 1 = 2x$

Step3: Multiply inner terms

$-1 \times 5x = -5x$

Step4: Multiply last terms

$-1 \times 1 = -1$

Step5: Combine like terms

$10x^2 + 2x - 5x - 1 = 10x^2 - 3x - 1$

3) $(4n+8)(n-1)$

Step1: Multiply first terms

$4n \times n = 4n^2$

Step2: Multiply outer terms

$4n \times (-1) = -4n$

Step3: Multiply inner terms

$8 \times n = 8n$

Step4: Multiply last terms

$8 \times (-1) = -8$

Step5: Combine like terms

$4n^2 - 4n + 8n - 8 = 4n^2 + 4n - 8$

4) $(n+7)(n+3)$

Step1: Multiply first terms

$n \times n = n^2$

Step2: Multiply outer terms

$n \times 3 = 3n$

Step3: Multiply inner terms

$7 \times n = 7n$

Step4: Multiply last terms

$7 \times 3 = 21$

Step5: Combine like terms

$n^2 + 3n + 7n + 21 = n^2 + 10n + 21$

5) $(2x+1)(6x-5)$

Step1: Multiply first terms

$2x \times 6x = 12x^2$

Step2: Multiply outer terms

$2x \times (-5) = -10x$

Step3: Multiply inner terms

$1 \times 6x = 6x$

Step4: Multiply last terms

$1 \times (-5) = -5$

Step5: Combine like terms

$12x^2 - 10x + 6x - 5 = 12x^2 - 4x - 5$

6) $(4n-3)(n-1)$

Step1: Multiply first terms

$4n \times n = 4n^2$

Step2: Multiply outer terms

$4n \times (-1) = -4n$

Step3: Multiply inner terms

$-3 \times n = -3n$

Step4: Multiply last terms

$-3 \times (-1) = 3$

Step5: Combine like terms

$4n^2 - 4n - 3n + 3 = 4n^2 - 7n + 3$

7) $(7m-8)(m-6)$

Step1: Multiply first terms

$7m \times m = 7m^2$

Step2: Multiply outer terms

$7m \times (-6) = -42m$

Step3: Multiply inner terms

$-8 \times m = -8m$

Step4: Multiply last terms

$-8 \times (-6) = 48$

Step5: Combine like terms

$7m^2 - 42m - 8m + 48 = 7m^2 - 50m + 48$

8) $(8x+8)(3x+7)$

Step1: Multiply first terms

$8x \times 3x = 24x^2$

Step2: Multiply outer terms

$8x \times 7 = 56x$

Step3: Multiply inner terms

$8 \times 3x = 24x$

Step4: Multiply last terms

$8 \times 7 = 56$

Step5: Combine like terms

$24x^2 + 56x + 24x + 56 = 24x^2 + 80x + 56$

9) $(4n+1)(2n-1)$

Step1: Multiply first terms

$4n \times 2n = 8n^2$

Step2: Multiply outer terms

$4n \times (-1) = -4n$

Step3: Multiply inner terms

$1 \times 2n = 2n$

Step4: Multiply last terms

$1 \times (-1) = -1$

Step5: Combine like terms

$8n^2 - 4n + 2n - 1 = 8n^2 - 2n - 1$

10) $(6p-5)(2p-8)$

Step1: Multiply first terms

$6p \times 2p = 12p^2$

Step2: Multiply outer terms

$6p \times (-8) = -48p$

Step3: Multiply inner terms

$-5 \times 2p = -10p$

Step4: Multiply last terms

$-5 \times (-8) = 40$

Step5: Combine like terms

$12p^2 - 48p - 10p + 40 = 12p^2 - 58p + 40$

11) $(p+7)(3p-6)$

Step1: Multiply first terms

$p \times 3p = 3p^2$

Step2: Multiply outer terms

$p \times (-6) = -6p$

Step3: Multiply inner terms

$7 \times 3p = 21p$

Step4: Multiply last terms

$7 \times (-6) = -42$

Step5: Combine like terms

$3p^2 - 6p + 21p - 42 = 3p^2 + 15p - 42$

12) $(3x-3)^2$

Step1: Use square formula

$(a-b)^2 = a^2 - 2ab + b^2$

Step2: Substitute and expand

$(3x)^2 - 2(3x)(3) + 3^2 = 9x^2 - 18x + 9$

13) $(3x+2)(3x-7)$

Step1: Multiply first terms

$3x \times 3x = 9x^2$

Step2: Multiply outer terms

$3x \times (-7) = -21x$

Step3: Multiply inner terms

$2 \times 3x = 6x$

Step4: Multiply last terms

$2 \times (-7) = -14$

Step5: Combine like terms

$9x^2 - 21x + 6x - 14 = 9x^2 - 15x - 14$

14) $(7b+3)(2b+4)$

Step1: Multiply first terms

$7b \times 2b = 14b^2$

Step2: Multiply outer terms

$7b \times 4 = 28b$

Step3: Multiply inner terms

$3 \times 2b = 6b$

Step4: Multiply last terms

$3 \times 4 = 12$

Step5: Combine like terms

$14b^2 + 28b + 6b + 12 = 14b^2 + 34b + 12$

15) $(3k-7)(4k+6)$

Step1: Multiply first terms

$3k \times 4k = 12k^2$

Step2: Multiply outer terms

$3k \times 6 = 18k$

Step3: Multiply inner terms

$-7 \times 4k = -28k$

Step4: Multiply last terms

$-7 \times 6 = -42$

Step5: Combine like terms

$12k^2 + 18k - 28k - 42 = 12k^2 - 10k - 42$

16) $(4r+5)(3r-3)$

Step1: Multiply first terms

$4r \times 3r = 12r^2$

Step2: Multiply outer terms

$4r \times (-3) = -12r$

Step3: Multiply inner terms

$5 \times 3r = 15r$

Step4: Multiply last terms

$5 \times (-3) = -15$

Step5: Combine like terms

$12r^2 - 12r + 15r - 15 = 12r^2 + 3r - 15$

17) $(7x-8)(4x-3)$

Step1: Multiply first terms

$7x \times 4x = 28x^2$

Step2: Multiply outer terms

$7x \times (-3) = -21x$

Step3: Multiply inner terms

$-8 \times 4x = -32x$

Step4: Multiply last terms

$-8 \times (-3) = 24$

Step5: Combine like terms

$28x^2 - 21x - 32x + 24 = 28x^2 - 53x + 24$

18) $(8r-7)(3r-8)$

Step1: Multiply first terms

$8r \times 3r = 24r^2$

Step2: Multiply outer terms

$8r \times (-8) = -64r$

Step3: Multiply inner terms

$-7 \times 3r = -21r$

Step4: Multiply last terms

$-7 \times (-8) = 56$

Step5: Combine like terms

$24r^2 - 64r - 21r + 56 = 24r^2 - 85r + 56$

19) $(x+8)(5x-1)$

Step1: Multiply first terms

$x \times 5x = 5x^2$

Step2: Multiply outer terms

$x \times (-1) = -x$

Step3: Multiply inner terms

$8 \times 5x = 40x$

Step4: Multiply last terms

$8 \times (-1) = -8$

Step5: Combine like terms

$5x^2 - x + 40x - 8 = 5x^2 + 39x - 8$

20) $(7x-2)(4x+4)$

Step1: Multiply first terms

$7x \times 4x = 28x^2$

Step2: Multiply outer terms

$7x \times 4 = 28x$

Step3: Multiply inner terms

$-2 \times 4x = -8x$

Step4: Multiply last terms

$-2 \times 4 = -8$

Step5: Combine like terms

$28x^2 + 28x - 8x - 8 = 28x^2 + 20x - 8$

21) $(x+1)(3x-1)$

Step1: Multiply first terms

$x \times 3x = 3x^2$

Step2: Multiply outer terms

$x \times (-1) = -x$

Step3: Multiply inner terms

$1 \times 3x = 3x$

Step4: Multiply last terms

$1 \times (-1) = -1$

Step5: Combine like terms

$3x^2 - x + 3x - 1 = 3x^2 + 2x - 1$

22) $(8m-3)^2$

Step1: Use square formula

$(a-b)^2 = a^2 - 2ab + b^2$

Step2: Substitute and expand

$(8m)^2 - 2(8m)(3) + 3^2 = 64m^2 - 48m + 9$

23) $(b+6)(b-6)$

Step1: Use difference of squares

$(a+b)(a-b)=a^2-b^2$

Step2: Substitute and expand

$b^2 - 6^2 = b^2 - 36$

24) $(6x-4)(7x-7)$

Step1: Multiply first terms

$6x \times 7x = 42x^2$

Step2: Multiply outer terms

$6x \times (-7) = -42x$

Step3: Multiply inner terms

$-4 \times 7x = -28x$

Step4: Multiply last terms

$-4 \times (-7) = 28$

Step5: Combine like terms

$42x^2 - 42x - 28x + 28 = 42x^2 - 70x + 28$

Answer:

1. $15r^2 + 52r + 32$
2. $10x^2 - 3x - 1$
3. $4n^2 + 4n - 8$
4. $n^2 + 10n + 21$
5. $12x^2 - 4x - 5$
6. $4n^2 - 7n + 3$
7. $7m^2 - 50m + 48$
8. $24x^2 + 80x + 56$
9. $8n^2 - 2n - 1$
10. $12p^2 - 58p + 40$
11. $3p^2 + 15p - 42$
12. $9x^2 - 18x + 9$
13. $9x^2 - 15x - 14$
14. $14b^2 + 34b + 12$
15. $12k^2 - 10k - 42$
16. $12r^2 + 3r - 15$
17. $28x^2 - 53x + 24$
18. $24r^2 - 85r + 56$
19. $5x^2 + 39x - 8$
20. $28x^2 + 20x - 8$
21. $3x^2 + 2x - 1$
22. $64m^2 - 48m + 9$
23. $b^2 - 36$
24. $42x^2 - 70x + 28$