Question

1. $(4p - 1)^2$ 14) $(7x - 6)(5x + 6)$ 15) $(6n + 3)(6n - 4)$ 16) $(8n + 1)(6n - 3)$ 17) $(6k + 5)(5k + 5)$ 18) $(3x - 4)(4x + 3)$ 19) $(4a + 2)(6a^2 - a + 2)$ 20) $(7k - 3)(k^2 - 2k + 7)$ 21) $(7r^2 - 6r - 6)(2r - 4)$ 22) $(n^2 + 6n - 4)(2n - 4)$ 23) $(6n^2 - 6n - 5)(7n^2 + 6n - 5)$

Explanation:

Step1: Expand using square of binomial

$(4p-1)^2 = (4p)^2 - 2(4p)(1) + 1^2$
$=16p^2 -8p +1$

Step2: Expand using FOIL method

$(7x-6)(5x+6)=7x\cdot5x +7x\cdot6 -6\cdot5x -6\cdot6$
$=35x^2 +42x -30x -36$
$=35x^2 +12x -36$

Step3: Expand using FOIL method

$(6n+3)(6n-4)=6n\cdot6n +6n\cdot(-4) +3\cdot6n +3\cdot(-4)$
$=36n^2 -24n +18n -12$
$=36n^2 -6n -12$

Step4: Expand using FOIL method

$(8n+1)(6n-3)=8n\cdot6n +8n\cdot(-3) +1\cdot6n +1\cdot(-3)$
$=48n^2 -24n +6n -3$
$=48n^2 -18n -3$

Step5: Expand using FOIL method

$(6k+5)(5k+5)=6k\cdot5k +6k\cdot5 +5\cdot5k +5\cdot5$
$=30k^2 +30k +25k +25$
$=30k^2 +55k +25$

Step6: Expand using FOIL method

$(3x-4)(4x+3)=3x\cdot4x +3x\cdot3 -4\cdot4x -4\cdot3$
$=12x^2 +9x -16x -12$
$=12x^2 -7x -12$

Step7: Distribute each term

$(4a+2)(6a^2 -a +2)=4a(6a^2 -a +2)+2(6a^2 -a +2)$
$=24a^3 -4a^2 +8a +12a^2 -2a +4$
$=24a^3 +8a^2 +6a +4$

Step8: Distribute each term

$(7k-3)(k^2 -2k +7)=7k(k^2 -2k +7)-3(k^2 -2k +7)$
$=7k^3 -14k^2 +49k -3k^2 +6k -21$
$=7k^3 -17k^2 +55k -21$

Step9: Distribute each term

$(7r^2 -6r -6)(2r -4)=7r^2(2r-4)-6r(2r-4)-6(2r-4)$
$=14r^3 -28r^2 -12r^2 +24r -12r +24$
$=14r^3 -40r^2 +12r +24$

Step10: Distribute each term

$(n^2 +6n -4)(2n -4)=n^2(2n-4)+6n(2n-4)-4(2n-4)$
$=2n^3 -4n^2 +12n^2 -24n -8n +16$
$=2n^3 +8n^2 -32n +16$

Step11: Distribute each term

$(6n^2 -6n -5)(7n^2 +6n -5)=6n^2(7n^2+6n-5)-6n(7n^2+6n-5)-5(7n^2+6n-5)$
$=42n^4 +36n^3 -30n^2 -42n^3 -36n^2 +30n -35n^2 -30n +25$
$=42n^4 -6n^3 -101n^2 +25$

Answer:

1. $16p^2 -8p +1$
2. $35x^2 +12x -36$
3. $36n^2 -6n -12$
4. $48n^2 -18n -3$
5. $30k^2 +55k +25$
6. $12x^2 -7x -12$
7. $24a^3 +8a^2 +6a +4$
8. $7k^3 -17k^2 +55k -21$
9. $14r^3 -40r^2 +12r +24$
10. $2n^3 +8n^2 -32n +16$
11. $42n^4 -6n^3 -101n^2 +25$