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### High School Mathematics5.5 Revision of Algebraic Expressions - V

 Examples: Expand, (2x + y + 3z)2. Given that, (2x + y + 3z)2, this is in the form of (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca Here a = 2x, b = y and c = 3z. = (2x)2 + y2 + (3z)2 + 2.2x.y + 2.y.3z + 2.3z.2x = 4x2 + y2 + 9z2 + 4xy + 6yz + 12xz Expand, 27x3 + y3. Given that, 27x3 + y3, We write this as (3x)3 + (y)3, this is in the form of a3 + b3 = (a+b)(a2 - ab + b2) Here, a = 3x and b = 2y = (3x + 2y) ((3x)2 - 3x.2y - (2y)2) = (3x + 2y)(9x2 - 6xy + 4y2) Expand, 8x3 - y3. Given that, 8x3 - y3 we can write this as (2x)3 - (y)3. This is in the form of a3 - b3 = (a - b)(a2 + ab + b2), here, a = 2x, and b = y = (2x - y)((2x)2 + 2x.y + y2) = (2x - y)(4x2 + 2xy + y2) Directions: Solve the following problems. Also write at least 10 examples of your own.
 Q 1: Expand, 27x3 - 125y3.(3x - 5y)(9x2 + 15xy + 9y2)(3x - 5y)(9x2 + 15xy + 25y2)(3x - 5y)(9x2 + 10xy + 25y2) Q 2: Expand, 8x3 - 64y3.(2x - 4y)(4x2 + 12xy + 16y2)(2x - 4y)(4x2 + 6xy + 16y2)(2x - 4y)(4x2 + 8xy + 16y2) Q 3: Expand, 8x3 + 125y3.(2x + 5y)(4x2 - 10xy + 25y2)(2x + 5y)(4x2 - 12xy + 25y2)(2x + 5y)(4x2 - 15xy + 25y2) Q 4: Expand, (2x + y - 3z)2.4x2 + y2 + 9z2 + 4xy - 12yz - 12xz4x2 + y2 + 9z2 + 4xy - 6yz - 12xz4x2 + y2 + 9z2 + 6xy - 6yz - 12xz Q 5: Expand, (x + 2y + 3z)2.x2 + 4y2 + 9z2 + 4xy + 12xz + 12yzx2 + 4y2 + 9z2 + 4xy + 6xz + 12yzx2 + 4y2 + 9z2 + 4xy + 6xz + 6yz Q 6: Expand, (x - 3y + 2z)2.x2 + 9y2 + 4z2 - 4xy - 12yz + 4xzx2 + 9y2 + 4z2 - 6xy - 6yz + 4xzx2 + 9y2 + 4z2 - 6xy - 12yz + 4xz Question 7: This question is available to subscribers only! Question 8: This question is available to subscribers only!