Simplify:
$(a b + b c)^{2} - 2 a b^{2} c$

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Solution

$(a b + b c)^{2} - 2 a b^{2} c$
$= (a b)^{2} + 2 \times a b \times b c + (b c)^{2} - 2 a b^{2} c$
$[U s i n g i d e n t i t y (a + b)^{2} = a^{2} + 2 a b + b^{2}] = a^{2} b^{2} + 2 a b^{2} c + b^{2} c^{2} - 2 a b^{2} c = a^{2} b^{2} + b^{2} c^{2}$

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(a b + b c)^{2} - 2 a b^{2} c

Question 4(vi)
Simplify:
$(a b + b c)^{2} - 2 a b^{2} c$

Question 4(vi)
Simplify:
$(a b + b c)^{2} - 2 a b^{2} c$

(a b + b c)^{2} - 2 a b^{2} c

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

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