Question 22 of 27intermediate🔧 ApplyNumerical6 marks

Use either a suitable identity or the distributive property to find each of the following products. (i) (p−1)(p+11)(p - 1) (p + 11) (ii) (3a−9b)(3a+9b)(3a - 9b) (3a + 9b) (iii) −(2y+5)(3y+4)-(2y + 5) (3y + 4) (iv) (6x+5y)2(6x + 5y)^2 (v) (2x−12)2(2x - \frac{1}{2})^2 (vi) (7p)×(3r)×(p+2)(7p) \times (3r) \times (p + 2)

(i)
Answer

p2+10p−11p^2 + 10p - 11

(ii)
Answer

9a2−81b29a^2 - 81b^2

(iii)
Answer

−6y2−23y−20-6y^2 - 23y - 20

(iv)
Answer

36x2+60xy+25y236x^2 + 60xy + 25y^2

(v)
Answer

4x2−2x+144x^2 - 2x + \frac{1}{4}

(vi)
Answer

21p2r+42pr21p^2r + 42pr

Explanation

(i) Distribute: p2+11p−p−11=p2+10p−11p^2 + 11p - p - 11 = p^2 + 10p - 11 (ii) Use Identity 1C: (3a)2−(9b)2=9a2−81b2(3a)^2 - (9b)^2 = 9a^2 - 81b^2 (iii) Distribute then negate: −(6y2+23y+20)=−6y2−23y−20-(6y^2 + 23y + 20) = -6y^2 - 23y - 20 (iv) Use Identity 1A: (6x)2+2(6x)(5y)+(5y)2=36x2+60xy+25y2(6x)^2 + 2(6x)(5y) + (5y)^2 = 36x^2 + 60xy + 25y^2 (v) Use Identity 1B: (2x)2−2(2x)(12)+(12)2=4x2−2x+14(2x)^2 - 2(2x)(\frac{1}{2}) + (\frac{1}{2})^2 = 4x^2 - 2x + \frac{1}{4} (vi) First multiply: 21pr21pr, then distribute: 21pr(p+2)=21p2r+42pr21pr(p + 2) = 21p^2r + 42pr

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