Question

Simplify. (i) (a2 − b2)^2 (ii) (2x +5)^2 − (2x − 5)^2 (iii) (7m − 8n)^2 + (7m + 8n)^2 (iv) (4m + 5n)^2 + (5m + 4n)2 (v) (2.5p − 1.5q)2 − (1.5p − 2.5q)2 (vi) (ab + bc)2 − 2ab2c (vii) (m2 − n2m)2 + 2m3n2

Answer 1

Solution:

$1) \: \: ( { {a}^{2} - {b}^{2}) }^{2} \\ \\ formula \: {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ \: ( { {a}^{2} - {b}^{2}) }^{2} = {a}^{4} + {b}^{4} - 2 {a}^{2} {b}^{2}$
$2) {(2x + 5)}^{2} - ( {2x - 5)}^{2} \\ \\ format : {a}^{2} - {b}^{2} = (a + b)(a - b) \\ \\ {(2x + 5)}^{2} - ( {2x - 5)}^{2} = (2x + 5 + 2x - 5)(2x + 5 - 2x + 5) \\ \\ = (4x)(10) \\ \\ = 40x$
(iii) (7m − 8n)^2 + (7m + 8n)^2

$formula \\ \\ ( {x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy \\ \\ ( {x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy \\ \\ ( {7m - 8n)}^{2} = 49 {m}^{2} + 64{n}^{2} - 112mn \\ \\ ( {7m + 8n)}^{2} = 49 {m}^{2} + 64{n}^{2} + 112mn \\ \\ ( {7m - 8n)}^{2} + ( {7m + 8n)}^{2} = 49 {m}^{2} + 64{n}^{2} - 112mn + 49 {m}^{2} + 64{n}^{2} + 112mn \\ \\ = 98 {m}^{2} + 128 {n}^{2}$
iv) (4m + 5n)^2 + (5m + 4n)^2

$( {4m + 5n)}^{2} = 16 {m}^{2} + 25 {n}^{2} + 40mn \\ \\ ( {5m + 4n)}^{2} = 25 {m}^{2} + 16 {n}^{2} + 40mn \\ \\( {4m + 5n)}^{2} + ( {5m + 4n)}^{2} = 16 {m}^{2} + 25 {n}^{2} + 40mn + 25 {m}^{2} + 16 {n}^{2} + 40mn \\ \\ = 41 {m}^{2} + 41 {n}^{2} + 80mn$
(v) (2.5p − 1.5q)^2 − (1.5p − 2.5q)^2

${(2.5p - 1.5q)}^{2} = 6.25 {p}^{2} + 2.25 {q}^{2} - 7.5pq \\ \\ {(2.5p - 1.5q)}^{2} - {(2.5p - 1.5q)}^{2} = \\ \\ = 6.25 {p}^{2} + 2.25 {q}^{2} - 7.5pq - ( 6.25 {p}^{2} + 2.25 {q}^{2} - 7.5pq) \\ \\ = 6.25 {p}^{2} + 2.25 {q}^{2} - 7.5pq - 6.25 {p}^{2} - 2.25 {q}^{2} + 7.5pq \\ \\ = 15pq$
Please check the expression of last two and post them again correctly.

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