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(x2- y2)2 + 4x2y2(b) (0.5p -– 1.5q)2 – (0.5p – 1.5q)2 +p2q2(c) 39n3(50n2 – 98 ) ÷ 26n2(5n – 7)(d) 44(p4 – 5p3 – 24p2) ÷ 11p(p – 8)(e) 9p²q² (3z – 12) ÷ 27pq(z – 4)(f) (4x2 – 100) ÷ 6(x + 5)

Question

(x2- y2)2 + 4x2y2(b) (0.5p -– 1.5q)2 – (0.5p – 1.5q)2 +p2q2(c) 39n3(50n2 – 98 ) ÷ 26n2(5n – 7)(d) 44(p4 – 5p3 – 24p2) ÷ 11p(p – 8)(e) 9p²q² (3z – 12) ÷ 27pq(z – 4)(f) (4x2 – 100) ÷ 6(x + 5)

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Solution

To solve the given expressions step by step:

(a) (x^2 - y^2)^2 + 4x^2y^2 = (x^4 - 2x^2y^2 + y^4) + 4x^2y^2 = x^4 - 2x^2y^2 + y^4 + 4x^2y^2 = x^4 + 2x^2y^2 + y^4

(b) (0.5p - 1.5q)^2 - (0.5p - 1.5q)^2 + p^2q^2 = 0 + p^2q^2 = p^2q^2

(c) 39n^3(50n^2 - 98) ÷ 26n^2(5n - 7) = (39n^3 * 2(25n^2 - 49)) ÷ (13n^2 * (5n - 7)) = (78n^3(25n^2 - 49)) ÷ (13n^2(5n - 7)) = (78n^3 * 25n^2 - 78n^3 * 49) ÷ (13n^2 * 5n - 13n^2 * 7) = (1950n^5 - 3822n^3) ÷ (65n^3 - 91n^2)

(d) 44(p^4 - 5p^3 - 24p^2) ÷ 11p(p - 8) = 4(p^4 - 5p^3 - 24p^2) ÷ p(p - 8) = 4p^3 - 20p^2 - 96p ÷ p^2 - 8p = 4p^2 - 20p - 96 ÷ p - 8

(e) 9p^2q^2 (3z - 12) ÷ 27pq(z - 4) = 9p^2q^2 * 3(z - 4) ÷ 27pq(z - 4) = 27p^2q^2(z - 4) ÷ 27pq(z - 4) = p^2q^2

(f) (4x^2 - 100) ÷ 6(x + 5) = 4(x^2 - 25) ÷ 6(x + 5) = 4(x - 5)(x + 5) ÷ 6(x + 5) = 4(x - 5) ÷ 6 = (2/3)(x - 5)

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1.    (x+2) (x2-4x+3)__              2.    (x-1) ( x2-8x+7)__              3.    (x-3y) ( x2-5xy+6y2)__              4.    (x+8) (x-1)_                5.    (2m+3n) (4m-5n)__              6.    (a+6) (a-5)_               7.    (x+4) (x-2)__             8.    (3a+7b) (5a-4b)           9.    (5m2-6m+10)  – (-m2+7m+8)__           10.    (2x2+4x+9) - ( x2-5x-6)           11.  6a + 12 / 3            12.    4x2-8x+12x3 / 4x

Factorize :i. 3x2y+9xy2–15xy ii. 2222 cb4916ba361 iii. 16x2–24yz–9y2–16z2 iv. (x–2y)2–6(x–2y)+5

4xy 2 −2x 2 y+(−4yx 2 +3y 2 x)?

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