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Factorise: 9x2 + 16y2 + 25z2 + 24xy + 40yz + 30xz
(3x + 4y + 5z) (3x − 4y + 5z)
(3x + 4y − 5z) (3x + 4y + 5z)
(3x − 4y + 5z) (3x + 4y + 5z)
(3x + 4y + 5z) (3x + 4y + 5z)
9x2 + 16y2 + 25z2 + 24xy + 40yz + 30xz
= (3x)2 + (4y)2 + (5z)2 + 24xy + 40yz + 30xz
We know that
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac
∴ (3x)2+ (4y)2 + (5z)2 + 24xy + 40yz + 30xz = (3x + 4y + 5z)2
∴ 9x2 + 16y2 + 25z2 + 24xy + 40yz + 30xz
= (3x + 4y + 5z) (3x + 4y + 5z)
Find the value of 97 × 103.
9918
9991
8901
7671
97 × 103 = (100 - 3)(100 + 3)
= 1002 − 32 … since a2 − b2 = (a - b) (a + b)
= 10000 - 9
= 9991
Find the value of (m - 4) (m + 3).
m2 - m - 12
m2 - 3m - 12
m2 − 7m - 12
m2 + m - 12
(m - 4) (m + 3) = m2 + (−4 + 3)m + (−4 × 3)
= m2 − m − 12 … since (x + a) (x + b) = x2 + (a + b)x + ab
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