Question 12 of 43intermediate🔧 ApplyFill in the Blanks3 marks

Fill in the blanks with the appropriate expressions to make the equation true. (px + a)(qx + b) = ()x2x^{2} + ()x + ____. Also, verify your answer using the distributive property.

Correct Answer

pq, pb + aq, ab

Exercise: Fill in the blanks | Q: 1 | (Chapter: 13)
For More Understanding

Explanation

The question requires expanding the product of two binomials using the distributive property. By multiplying each term of the first binomial by each term of the second binomial, we get px(qx) + px(b) + a(qx) + a(b). Multiplying the terms yields pqx2pqx^{2} + pbx + aqx + ab. Finally, combining the like terms (pbx and aqx) gives the expanded form pqx2pqx^{2} + (pb + aq)x + ab, which provides the expressions for the three blanks respectively.

Solution Steps

  1. Step 1: Apply the distributive property to expand the product: (px + a)(qx + b) = px(qx + b) + a(qx + b)

  2. Step 2: Distribute the terms again: = px(qx) + px(b) + a(qx) + a(b)

  3. Step 3: Multiply the terms: = pqx2pqx^{2} + pbx + aqx + ab

  4. Step 4: Combine the like terms for x: = pqx2pqx^{2} + (pb + aq)x + ab

  5. Step 5: Match the resulting expression with ()x2x^{2} + ()x + ____ to identify the blanks as pq, pb + aq, and ab.

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