We Distribute Yet Things Multiply — Practice

Question 1

Simplify: 3x(2x + 5)

Accepted Answer

✦ Answer: 3x × 2x + 3x × 5 = 6x² + 15x.

Question 2

Expand (x + 4)².

Accepted Answer

✦ Answer: (a+b)² = a² + 2ab + b². Here a=x, b=4. So (x+4)² = x² + 2(x)(4) + 4² = x² + 8x + 16.

Question 3

Multiply (3x − 2)(2x + 5).

Accepted Answer

Step 1 — Apply FOIL.
  F: 3x × 2x = 6x²
  O: 3x × 5 = 15x
  I: −2 × 2x = −4x
  L: −2 × 5 = −10

Step 2 — Combine like terms.
  6x² + (15x − 4x) − 10
  = 6x² + 11x − 10

Step 3 — Verify with substitution.
  Let x = 1: (3−2)(2+5) = 1 × 7 = 7
  6(1) + 11(1) − 10 = 6 + 11 − 10 = 7 ✓

✦ Answer: 6x² + 11x − 10.

Question 4

Compute 97² using algebraic identity.

Accepted Answer

Step 1 — Express 97 as 100 − 3.
  97 = 100 − 3

Step 2 — Apply (a − b)² identity.
  97² = (100 − 3)² = 100² − 2(100)(3) + 3²

Step 3 — Compute.
  = 10000 − 600 + 9
  = 9409

Step 4 — Verify by direct multiplication.
  97 × 97 = 9409 ✓

✦ Answer: 97² = 9409. This is much faster than direct multiplication.

Question 5

Factorise: (a) x² + 9x + 20 (b) 25y² − 49 (c) 4p² + 12p + 9

Accepted Answer

Part (a) — Split the middle term.
  Look for two numbers with: sum = 9, product = 20.
  Try 4 and 5: 4+5 = 9 ✓; 4×5 = 20 ✓.
  x² + 9x + 20 = (x + 4)(x + 5).

Part (b) — Difference of squares.
  25y² − 49 = (5y)² − 7² = (5y + 7)(5y − 7).

Part (c) — Perfect square trinomial.
  Recognise: 4p² = (2p)², 9 = 3², 12p = 2(2p)(3).
  Matches a² + 2ab + b² = (a+b)².
  4p² + 12p + 9 = (2p + 3)².

Step — Verify each.
  (a) (x+4)(x+5) = x² + 5x + 4x + 20 = x² + 9x + 20 ✓
  (b) (5y+7)(5y−7) = 25y² − 49 ✓
  (c) (2p+3)² = 4p² + 12p + 9 ✓

✦ Answer: (a) (x+4)(x+5). (b) (5y+7)(5y−7). (c) (2p+3)².

Practice — We Distribute Yet Things Multiply

Sign in to save attempts to your dashboard and track your accuracy over time

Find a verified tutor

Join a live course

Browse coaching centres

About

Categories

Support

Documentation

Get Study Tips & Updates

Download Our App

Download for iOS

Download for Android

Popular Cities