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Use the identity (x+a)(x+b)=x^2+(a+b)x+a...

Use the identity `(x+a)(x+b)=x^2+(a+b)x+ab` to find the following products.
(i) `(x+3)(x+7)`
(ii) `(4x+5)(4x+1)`
(iii) `(4x+5)(4x+1)`
(iv) `(4x+5)(4x-1)`
(v) `(2x+5y)(2x+3y)`
(vi) `(2a^2+9)(2a^2+5)`
(vii) `(xyz-4)(xyz-2)`

Text Solution

Verified by Experts

Using the algebraic identity `(x + a)(x + b) = x^2 + (a + b)x + ab `
`(i) (x + 3)(x + 7)`
`= x^2 + (3 + 7)x + (3)(7)`
`= x^2 + 10x + 21`
`(ii) (4x + 5)(4x + 1)`
`= (4x)^2 + (5 + 1)(4x) + (5)(1)`
`= 16x^2 + 24x + 5`
`(iii) (4x - 5)(4x - 1)`
...
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