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(4m + 5n) 2 + (5m + 4n) 2 [(4m) 2 - 2(4m)(5n) + (5n) 2 ] + [(5m) 2 + 2(5m)(4n) + (4n) 2 ] = 16m 2 + 20mn + 25n 2 + 25m 2 + 40mn + 16n 2 = (16 + 25)m 2 + (40 + 40) mn + (25 + 16)n 2 = 41m 2 + 80mn + 41n 2

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Algebraic Expressions and Identities

Short Answer Type

111.

Find the following squares by using the identities.

(xy + 3z)²

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112.

Find the following squares by using the identities.

(6x² - 5y)²

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113.

Find the following squares by using the identities.

$space space space space space space space space space space space open parentheses 2 over 3 straight m space plus space 3 over 2 straight n close parentheses squared$

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114.

Find the following squares by using the identities.

(0.4p - 0.5q)²

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115.

Find the following squares by using the identities.

(2xy + 5y)²

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116.

Simplify:

(a²- b²)²

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117.

Simplify:

(2x + 5)²- (2x - 5)²

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118.

Simplify:

(7m - 8n)²- (7m + 8n)²

302 Views

119.
Simplify:

(4m + 5n)²+ (5m + 4n)²

(4m + 5n)²+ (5m + 4n)²
[(4m)²- 2(4m)(5n) + (5n)²] + [(5m)²+ 2(5m)(4n) + (4n)²]
= 16m²+ 20mn + 25n²+ 25m²+ 40mn + 16n²= (16 + 25)m²+ (40 + 40) mn + (25 + 16)n²
= 41m²+ 80mn + 41n²